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Calculus

  • 200 videos
  • 191,318 views
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Topics covered in the first two or three semesters of college calculus. Everything from limits to derivatives to integrals to vector calculus. Should understand the topics in the pre-calculus playlist first (the limit videos are in both playlists)

Topics covered in the first two or three semesters of college calculus. Everything from limits to derivatives to integrals to vector calculus. Should understand the topics in the pre-calculus playlist first (the limit videos are in both playlists)
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    Newton Leibniz and Usain Bolt

    by Khan Academy 340,686 views

    Learn more: http://www.khanacademy.org/video?v=EKvHQc3QEow
    Why we study differential calculus

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    Introduction to Limits (HD)

    by Khan Academy 953,470 views

    Learn more: http://www.khanacademy.org/video?v=riXcZT2ICjA
    Introduction to Limits (HD)

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    Introduction to Limits

    by Khan Academy 771,809 views

    Learn more: http://www.khanacademy.org/video?v=W0VWO4asgmk
    Introduction to the intuition behind limits

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    Limit Examples (part 1)

    by Khan Academy 682,783 views

    Learn more: http://www.khanacademy.org/video?v=GGQngIp0YGI
    Some limit exercises

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    Limit Examples (part 2)

    by Khan Academy 452,152 views

    Learn more: http://www.khanacademy.org/video?v=YRw8udexH4o
    More limit examples

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    Limit Examples (part3)

    by Khan Academy 414,912 views

    Learn more: http://www.khanacademy.org/video?v=gWSDDopD9sk
    More limit examples

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    Limit Examples w/ brain malfunction on first prob (part 4)

    by Khan Academy 310,567 views

    Learn more: http://www.khanacademy.org/video?v=xjkSE9cPqzo
    3 interesting limit examples (correct answer for problem 1 is 3/16 (6/(4*8) NOT 6/(4+8))

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    Squeeze Theorem

    by Khan Academy 360,955 views

    Learn more: http://www.khanacademy.org/video?v=igJdDN-DPgA
    Intuition (but not a proof) of the Squeeze Theorem.

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    Proof: lim (sin x)/x

    by Khan Academy 451,914 views

    Learn more: http://www.khanacademy.org/video?v=Ve99biD1KtA
    Using the squeeze theorem to prove that the limit as x approaches 0 of (sin x)/x =1

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    More Limits

    by Khan Academy 194,779 views

    Learn more: http://www.khanacademy.org/video?v=rkeU8_4nzKo
    More limit examples

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    Epsilon Delta Limit Definition 1

    by Khan Academy 297,762 views

    Learn more: http://www.khanacademy.org/video?v=-ejyeII0i5c
    Introduction to the Epsilon Delta Definition of a Limit.

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    Epsilon Delta Limit Definition 2

    by Khan Academy 200,013 views

    Learn more: http://www.khanacademy.org/video?v=Fdu5-aNJTzU
    Using the epsilon delta definition to prove a limit

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    Calculus: Derivatives 1 (new HD version)

    by Khan Academy 619,705 views

    Learn more: http://www.khanacademy.org/video?v=ANyVpMS3HL4
    Calculus-Derivative: Understanding that the derivative is just the slope of a curve at a point (or the slope of the tangent line)

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    Calculus: Derivatives 2 (new HD version)

    by Khan Academy 365,317 views

    Learn more: http://www.khanacademy.org/video?v=IePCHjMeFkE
    Calculus-Derivative: Finding the slope (or derivative) of a curve at a particular point.

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    Calculus: Derivatives 2.5 (new HD version)

    by Khan Academy 285,316 views

    Learn more: http://www.khanacademy.org/video?v=HEH_oKNLgUU
    Calculus-Derivative: Finding the derivative of y=x^2

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    Derivative Intuition Module

    by Khan Academy 106,934 views

    Learn more: http://www.khanacademy.org/video?v=HtvikVD9aa0
    Sal walking through the derivative intuition module made by Ben Eater

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    Calculus: Derivatives 1

    by Khan Academy 790,853 views

    Learn more: http://www.khanacademy.org/video?v=rAof9Ld5sOg
    Finding the slope of a tangent line to a curve (the derivative). Introduction to Calculus.

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    Calculus: Derivatives 2

    by Khan Academy 301,278 views

    Learn more: http://www.khanacademy.org/video?v=ay8838UZ4nM
    More intuition of what a derivative is. Using the derivative to find the slope at any point along f(x)=x^2

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    Calculus: Derivatives 3

    by Khan Academy 321,533 views

    Learn more: http://www.khanacademy.org/video?v=z1lwai-lIzY
    Determining the derivatives of simple polynomials.

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    The Chain Rule

    by Khan Academy 548,834 views

    Learn more: http://www.khanacademy.org/video?v=XIQ-KnsAsbg
    Part 4 of derivatives. Introduction to the chain rule.

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    Chain Rule Examples

    by Khan Academy 338,760 views

    Learn more: http://www.khanacademy.org/video?v=6_lmiPDedsY
    Examples using the Chain Rule

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    Even More Chain Rule

    by Khan Academy 263,720 views

    Learn more: http://www.khanacademy.org/video?v=DYb-AN-lK94
    Even more examples using the chain rule.

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    Product Rule

    by Khan Academy 282,865 views

    Learn more: http://www.khanacademy.org/video?v=h78GdGiRmpM
    The product rule. Examples using the Product and Chain rules.

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    Quotient Rule

    by Khan Academy 257,699 views

    Learn more: http://www.khanacademy.org/video?v=E_1gEtiGPNI
    Why the quotient rule is the same thing as the product rule. Introduction to the derivative of e^x, ln x, sin x, cos x, and tan x

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    Derivatives (part 9)

    by Khan Academy 203,387 views

    Learn more: http://www.khanacademy.org/video?v=aEP4C_kvcO4
    More examples of taking derivatives

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    Proof: d/dx(x^n)

    by Khan Academy 140,103 views

    Learn more: http://www.khanacademy.org/video?v=dZnc3PtNaN4
    Proof that d/dx(x^n) = n*x^(n-1)

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    Proof: d/dx(sqrt(x))

    by Khan Academy 81,273 views

    Learn more: http://www.khanacademy.org/video?v=789aMeepbxI
    Proof that d/dx (x^.5) = .5x^(-.5)

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    Proof: d/dx(ln x) = 1/x

    by Khan Academy 153,451 views

    Learn more: http://www.khanacademy.org/video?v=yUpDRpkUhf4
    Taking the derivative of ln x

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    Proof: d/dx(e^x) = e^x

    by Khan Academy 113,179 views

    Learn more: http://www.khanacademy.org/video?v=sSE6_fK3mu0
    Proof that the derivative of e^x is e^x.

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    Proofs of Derivatives of Ln(x) and e^x

    by Khan Academy 124,747 views

    Learn more: http://www.khanacademy.org/video?v=3nQejB-XPoY
    Doing both proofs in the same video to clarify any misconceptions that the original proof was "circular".

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    Extreme Derivative Word Problem (advanced)

    by Khan Academy 105,223 views

    Learn more: http://www.khanacademy.org/video?v=viaPc8zDcRI
    A difficult but interesting derivative word problem

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    Implicit Differentiation

    by Khan Academy 475,622 views

    Learn more: http://www.khanacademy.org/video?v=sL6MC-lKOrw
    Taking the derivative when y is defined implicitly.

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    Implicit Differentiation (part 2)

    by Khan Academy 182,117 views

    Learn more: http://www.khanacademy.org/video?v=PUsMyhds5S4
    A hairier implicit differentiation problem.

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    More implicit differentiation

    by Khan Academy 115,757 views

    Learn more: http://www.khanacademy.org/video?v=hrg1hCzg3W0
    2 more implicit differentiation examples

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    More chain rule and implicit differentiation intuition

    by Khan Academy 129,623 views

    Learn more: http://www.khanacademy.org/video?v=XHBkQW_XuA4
    More intuition behind the chain rule and how it applies to implicit differentiation.

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    Trig Implicit Differentiation Example

    by Khan Academy 100,503 views

    Learn more: http://www.khanacademy.org/video?v=6xvwyE67CeM
    Implicit differentiation example that involves the tangent function

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    Calculus: Derivative of x^(x^x)

    by Khan Academy 123,483 views

    Learn more: http://www.khanacademy.org/video?v=N5kkwVoAtkc
    Calculus: Derivative of x^(x^x)

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    Introduction to L'Hopital's Rule

    by Khan Academy 244,824 views

    Learn more: http://www.khanacademy.org/video?v=PdSzruR5OeE
    Introduction to L'Hopital's Rule

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    L'Hopital's Rule Example 1

    by Khan Academy 159,838 views

    Learn more: http://www.khanacademy.org/video?v=BiVOC3WocXs
    L'Hopital's Rule Example 1

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    L'Hopital's Rule Example 2

    by Khan Academy 103,834 views

    Learn more: http://www.khanacademy.org/video?v=FJo18AwLfuI
    L'Hopital's Rule Example 2

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    L'Hopital's Rule Example 3

    by Khan Academy 96,304 views

    Learn more: http://www.khanacademy.org/video?v=MeVFZjT-ABM
    L'Hopital's Rule Example 3

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    Maxima Minima Slope Intuition

    by Khan Academy 140,553 views

    Learn more: http://www.khanacademy.org/video?v=tpHz0gZfVss
    Intuition on what happens to the slope/derivative and second derivatives at local maxima and minima.

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    Inflection Points and Concavity Intuition

    by Khan Academy 164,242 views

    Learn more: http://www.khanacademy.org/video?v=dIE22eL6q90
    Understanding concave upwards and downwards portions of graphs and the relation to the derivative. Inflection point intuition

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    Monotonicity Theorem

    by Khan Academy 76,906 views

    Learn more: http://www.khanacademy.org/video?v=WrEcQsa-1ME
    Using the monotonicity theorem to determine when a function is increasing or decreasing.

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    Calculus: Maximum and minimum values on an interval

    by Khan Academy 258,376 views

    Learn more: http://www.khanacademy.org/video?v=gzmSKrwiG3g
    2 examples of finding the maximum and minimum points on an interval.

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    Calculus: Graphing Using Derivatives

    by Khan Academy 163,196 views

    Learn more: http://www.khanacademy.org/video?v=hIgnece9ins
    Graphing functions using derivatives.

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    Calculus Graphing with Derivatives Example

    by Khan Academy 85,332 views

    Learn more: http://www.khanacademy.org/video?v=zC_dTaEY2AY
    Using the first and second derivatives to identify critical points and inflection points and to graph the function.

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    Graphing with Calculus

    by Khan Academy 63,711 views

    Learn more: http://www.khanacademy.org/video?v=ojcp0GJKluM
    More graphing with calculus.

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    Optimization with Calculus 1

    by Khan Academy 255,832 views

    Learn more: http://www.khanacademy.org/video?v=Ef22yTJDUZI
    Find two numbers whose products is -16 and the sum of whose squares is a minimum.

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    Optimization with Calculus 2

    by Khan Academy 151,960 views

    Learn more: http://www.khanacademy.org/video?v=3GYv-BZYYdg
    Find the volume of the largest open box that can be made from a piece of cardboard 24 inches square by cutting equal squares from the corners and turning up the sides.

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    Optimization with Calculus 3

    by Khan Academy 115,638 views

    Learn more: http://www.khanacademy.org/video?v=i8Wtu-kdDC4
    A wire of length 100 centimeters is cut into two pieces; one is bent to form a square, and the other is bent to form an equilateral triangle. Where should the cut be made if (a) the sum of the two areas is to be a minimum; (b) a maximum? (Allow the possibility of no cut.)

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    Optimization Example 4

    by Khan Academy 91,050 views

    Learn more: http://www.khanacademy.org/video?v=T8sG4Sb3g7Y
    Minimizing the cost of material for an open rectangular box.

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    Introduction to rate-of-change problems

    by Khan Academy 191,378 views

    Learn more: http://www.khanacademy.org/video?v=Zyq6TmQVBxk
    Using derivatives to solve rate-of-change problems

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    Equation of a tangent line

    by Khan Academy 126,174 views

    Learn more: http://www.khanacademy.org/video?v=1KwW1v__T_0
    Finding the equation of the line tangent to f(x)=xe^x when x=1

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    Rates-of-change (part 2)

    by Khan Academy 112,041 views

    Learn more: http://www.khanacademy.org/video?v=xmgk8_l3lig
    Another (simpler) example of using the chain rule to determine rates-of-change

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    Ladder rate-of-change problem

    by Khan Academy 96,112 views

    Learn more: http://www.khanacademy.org/video?v=hD3U65CcZ0Q
    The classic falling ladder problem

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    Mean Value Theorem

    by Khan Academy 216,394 views

    Learn more: http://www.khanacademy.org/video?v=bGNMXfaNR5Q
    Intuition behind the Mean Value Theorem

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    The Indefinite Integral or Anti-derivative

    by Khan Academy 435,082 views

    Learn more: http://www.khanacademy.org/video?v=xRspb-iev-g
    An introduction to indefinite integration of polynomials.

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    Indefinite integrals (part II)

    by Khan Academy 299,103 views

    Learn more: http://www.khanacademy.org/video?v=mHvSYRUEWnE
    Examples of taking the indefinite integral (or anti-derivative) of polynomials.

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    Indefinite Integration (part III)

    by Khan Academy 273,135 views

    Learn more: http://www.khanacademy.org/video?v=77-najNh4iY
    Integration by doing the chain rule in reverse.

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    Indefinite Integration (part IV)

    by Khan Academy 225,269 views

    Learn more: http://www.khanacademy.org/video?v=VJ9VRUDQyK8
    Integration by substitution (or the reverse-chain-rule)

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    Indefinite Integration (part V)

    by Khan Academy 191,837 views

    Learn more: http://www.khanacademy.org/video?v=Pra6r20geXU
    Introduction to Integration by Parts (kind of the reverse-product rule)

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    Integration by Parts (part 6 of Indefinite Integration)

    by Khan Academy 245,367 views

    Learn more: http://www.khanacademy.org/video?v=ouYZiIh8Ctc
    Example using Integration by Parts

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    Indefinite Integration (part 7)

    by Khan Academy 149,548 views

    Learn more: http://www.khanacademy.org/video?v=F-OsMq7QKEQ
    Another example using integration by parts.

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    Another u-subsitution example

    by Khan Academy 150,504 views

    Learn more: http://www.khanacademy.org/video?v=IAbSeAk5RJU
    Finding the antiderivative using u-substitution.

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    Introduction to definite integrals

    by Khan Academy 300,881 views

    Learn more: http://www.khanacademy.org/video?v=0RdI3-8G4Fs
    Using the definite integral to solve for the area under a curve. Intuition on why the antiderivative is the same thing as the area under a curve.

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    Definite integrals (part II)

    by Khan Academy 206,819 views

    Learn more: http://www.khanacademy.org/video?v=6PaFm_Je5A0
    More on why the antiderivative and the area under a curve are essentially the same thing.

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    Definite Integrals (area under a curve) (part III)

    by Khan Academy 195,758 views

    Learn more: http://www.khanacademy.org/video?v=7wUHJ7JQ-gs
    More on why the antiderivative and the area under a curve are essentially the same thing.

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    Definite Integrals (part 4)

    by Khan Academy 146,567 views

    Learn more: http://www.khanacademy.org/video?v=11Bt6OhIeqA
    Examples of using definite integrals to find the area under a curve

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    Definite Integrals (part 5)

    by Khan Academy 124,485 views

    Learn more: http://www.khanacademy.org/video?v=CmXmRNFrtFw
    More examples of using definite integrals to calculate the area between curves

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    Definite integral with substitution

    by Khan Academy 147,593 views

    Learn more: http://www.khanacademy.org/video?v=CbUx0S8BCtA
    Solving a definite integral with substitution (or the reverse chain rule)

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    Integrals: Trig Substitution 1

    by Khan Academy 221,653 views

    Learn more: http://www.khanacademy.org/video?v=n4EK92CSuBE
    Example of using trig substitution to solve an indefinite integral

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    Integrals: Trig Substitution 2

    by Khan Academy 116,125 views

    Learn more: http://www.khanacademy.org/video?v=fD7MbnXbTls
    Another example of finding an anti-derivative using trigonometric substitution

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    Integrals: Trig Substitution 3 (long problem)

    by Khan Academy 89,475 views

    Learn more: http://www.khanacademy.org/video?v=sw2p2tUIFpc
    Example using trig substitution (and trig identities) to solve an integral.

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    Periodic Definite Integral

    by Khan Academy 43,031 views

    Learn more: http://www.khanacademy.org/video?v=CZdziIlYIfI
    2010 IIT JEE Paper 1 Problem 52 Periodic Definite Integral. The second term at about minute 14 should have a positive sign. Luckily, it doesn't effect the final answer!

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    Simple Differential Equations

    by Khan Academy 198,619 views

    Learn more: http://www.khanacademy.org/video?v=C8mudsCSmcU
    3 basic differential equations that can be solved by taking the antiderivatives of both sides.

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    Solid of Revolution (part 1)

    by Khan Academy 214,769 views

    Learn more: http://www.khanacademy.org/video?v=R_aqSL-q6_8
    Figuring out the volume of a function rotated about the x-axis.

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    Solid of Revolution (part 2)

    by Khan Academy 125,530 views

    Learn more: http://www.khanacademy.org/video?v=iUzfsUOl3-A
    The volume of y=sqrt(x) between x=0 and x=1 rotated around x-axis

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    Solid of Revolution (part 3)

    by Khan Academy 107,757 views

    Learn more: http://www.khanacademy.org/video?v=tqfU9mC2yFU
    Figuring out the equation for the volume of a sphere.

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    Solid of Revolution (part 4)

    by Khan Academy 94,854 views

    Learn more: http://www.khanacademy.org/video?v=OtmjNuiTHp0
    More volumes around the x-axis.

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    Solid of Revolution (part 5)

    by Khan Academy 116,706 views

    Learn more: http://www.khanacademy.org/video?v=NIdqkwocNuE
    Use the "shell method" to rotate about the y-axis

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    Solid of Revolution (part 6)

    by Khan Academy 86,355 views

    Learn more: http://www.khanacademy.org/video?v=F2psxMnGdUw
    Using the disk method around the y-axis.

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    Solid of Revolution (part 7)

    by Khan Academy 77,958 views

    Learn more: http://www.khanacademy.org/video?v=IZ8W-h764Cc
    Taking the revolution around something other than one of the axes.

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    Solid of Revolution (part 8)

    by Khan Academy 53,116 views

    Learn more: http://www.khanacademy.org/video?v=4Flj9plmKGQ
    The last part of the problem in part 7

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    Sequences and Series (part 1)

    by Khan Academy 429,359 views

    Learn more: http://www.khanacademy.org/video?v=VgVJrSJxkDk
    Introduction to the arithmetic and geometric series

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    Sequences and series (part 2)

    by Khan Academy 284,261 views

    Learn more: http://www.khanacademy.org/video?v=U_8GRLJplZg
    Finding the sum of an infinite geometric series.

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    Maclauren and Taylor Series Intuition

    by Khan Academy 186,862 views

    Learn more: http://www.khanacademy.org/video?v=epgwuzzDHsQ
    Approximating a function at 0 using a polynomial

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    Cosine Taylor Series at 0 (Maclaurin)

    by Khan Academy 75,069 views

    Learn more: http://www.khanacademy.org/video?v=WWe7pZjc4s8
    Approximating f(x)=cos x using a Maclauren Series (special case of a Taylor series at x=0)

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    Sine Taylor Series at 0 (Maclaurin)

    by Khan Academy 54,920 views

    Learn more: http://www.khanacademy.org/video?v=LlKvubIqHc8
    Sine Taylor Series at 0 (Maclaurin)

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    Taylor Series at 0 (Maclaurin) for e to the x

    by Khan Academy 69,240 views

    Learn more: http://www.khanacademy.org/video?v=JYQqml4-4q4
    Taylor Series at 0 (Maclaurin) for e to the x

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    Euler's Formula and Euler's Identity

    by Khan Academy 139,423 views

    Learn more: http://www.khanacademy.org/video?v=mgNtPOgFje0
    Rationale for Euler's Formula and Euler's Identity

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    Visualizing Taylor Series Approximations

    by Khan Academy 83,051 views

    Learn more: http://www.khanacademy.org/video?v=8dMLK2Wueaw
    Using Wolfram Alpha to approximate sin(x)

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    Generalized Taylor Series Approximation

    by Khan Academy 60,348 views

    Learn more: http://www.khanacademy.org/video?v=1LxhXqD3_CE
    Approximating a function around a non-zero x value

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    Visualizing Taylor Series for e^x

    by Khan Academy 37,236 views

    Learn more: http://www.khanacademy.org/video?v=AFMXixBVP-0
    Visualizing Taylor Series for e^x

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    Polynomial approximation of functions (part 1)

    by Khan Academy 128,185 views

    Learn more: http://www.khanacademy.org/video?v=sy132cgqaiU
    Using a polynomial to approximate a function at f(0).

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    Polynomial approximation of functions (part 2)

    by Khan Academy 50,426 views

    Learn more: http://www.khanacademy.org/video?v=3JG3qn7-Sac
    Approximating a function with a polynomial by making the derivatives equal at f(0) (Maclauren Series)

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    Approximating functions with polynomials (part 3)

    by Khan Academy 45,764 views

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    A glimpse of the mystery of the Universe as we approximate e^x with an infinite series.

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    Polynomial approximation of functions (part 4)

    by Khan Academy 41,236 views

    Learn more: http://www.khanacademy.org/video?v=gcJeg4SdIpU
    Approximating cos x with a Maclaurin series.

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    Polynomial approximations of functions (part 5)

    by Khan Academy 31,612 views

    Learn more: http://www.khanacademy.org/video?v=9AoDucUmO20
    MacLaurin representation of sin x

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    Polynomial approximation of functions (part 6)

    by Khan Academy 33,664 views

    Learn more: http://www.khanacademy.org/video?v=-gRNRBCG3Ow
    A pattern emerges!

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    Polynomial approximation of functions (part 7)

    by Khan Academy 44,417 views

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    The most amazing conclusion in mathematics!

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    Taylor Polynomials

    by Khan Academy 174,330 views

    Learn more: http://www.khanacademy.org/video?v=8SsC5st4LnI
    Approximating a function with a Taylor Polynomial

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    Exponential Growth

    by Khan Academy 154,764 views

    Learn more: http://www.khanacademy.org/video?v=JWfTckls59k
    Exponential growth involving bacteria (some calculus in part c).

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    AP Calculus BC Exams: 2008 1 a

    by Khan Academy 44,464 views

    Learn more: http://www.khanacademy.org/video?v=upO6Mh862PI
    Part 1a of the 2008 BC free response

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    AP Calculus BC Exams: 2008 1 b&c

    by Khan Academy 19,119 views

    Learn more: http://www.khanacademy.org/video?v=xPb6HLM3xEQ
    Parts b and c of problem 1 (free response)

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    AP Calculus BC Exams: 2008 1 c&d

    by Khan Academy 16,047 views

    Learn more: http://www.khanacademy.org/video?v=_l0Mfsu__gU
    parts c&d of problem 1 in the 2008 AP Calculus BC free response

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    AP Calculus BC Exams: 2008 1 d

    by Khan Academy 13,871 views

    Learn more: http://www.khanacademy.org/video?v=sPTuCE5zd3s
    Part 1d of the 2008 AP Calculus BC exam (free response)

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    Calculus BC 2008 2 a

    by Khan Academy 15,526 views

    Learn more: http://www.khanacademy.org/video?v=xvvI_QRYxBY
    2a of 2008 Calculus BC exam (free response)

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    Calculus BC 2008 2 b &c

    by Khan Academy 11,533 views

    Learn more: http://www.khanacademy.org/video?v=S4oOSgTj9C8
    Parts 2b and 2c of the 2008 BC exam (free response)

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    Calculus BC 2008 2d

    by Khan Academy 10,837 views

    Learn more: http://www.khanacademy.org/video?v=o_vMb655dFk
    Part 2d of the 2008 Calculus BC exam free-response section

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    Partial Derivatives

    by Khan Academy 234,209 views

    Learn more: http://www.khanacademy.org/video?v=1CMDS4-PKKQ
    Introduction to partial derivatives.

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    Partial Derivatives 2

    by Khan Academy 122,449 views

    Learn more: http://www.khanacademy.org/video?v=-u0mqFqpMNY
    More on partial derivatives

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    Gradient 1

    by Khan Academy 154,936 views

    Learn more: http://www.khanacademy.org/video?v=U7HQ_G_N6vo
    Introduction to the gradient

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    Gradient of a scalar field

    by Khan Academy 98,361 views

    Learn more: http://www.khanacademy.org/video?v=OB8b8aDGLgE
    Intuition of the gradient of a scalar field (temperature in a room) in 3 dimensions.

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    Divergence 1

    by Khan Academy 124,161 views

    Learn more: http://www.khanacademy.org/video?v=JAXyLhvZ-Vg
    Introduction to the divergence of a vector field.

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    Divergence 2

    by Khan Academy 59,640 views

    Learn more: http://www.khanacademy.org/video?v=tOX3RkH2guE
    The intuition of what the divergence of a vector field is.

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    Divergence 3

    by Khan Academy 51,404 views

    Learn more: http://www.khanacademy.org/video?v=U6Re4xT0o4w
    Analyzing a vector field using its divergence.

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    Curl 1

    by Khan Academy 79,929 views

    Learn more: http://www.khanacademy.org/video?v=Mt4dpGFVsYc
    Introduction to the curl of a vector field

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    Curl 2

    by Khan Academy 47,246 views

    Learn more: http://www.khanacademy.org/video?v=hTSyVgBa1T0
    The mechanics of calculating curl.

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    Curl 3

    by Khan Academy 42,239 views

    Learn more: http://www.khanacademy.org/video?v=fYzoiWIBjP8
    More on curl

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    Double Integral 1

    by Khan Academy 164,594 views

    Learn more: http://www.khanacademy.org/video?v=85zGYB-34jQ
    Introduction to the double integral

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    Double Integrals 2

    by Khan Academy 101,345 views

    Learn more: http://www.khanacademy.org/video?v=TdLD2Zh-nUQ
    Figuring out the volume under z=xy^2

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    Double Integrals 3

    by Khan Academy 70,799 views

    Learn more: http://www.khanacademy.org/video?v=z8BM6cHifPA
    Let's integrate dy first!

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    Double Integrals 4

    by Khan Academy 63,690 views

    Learn more: http://www.khanacademy.org/video?v=twT-WZChfZ8
    Another way to conceptualize the double integral.

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    Double Integrals 5

    by Khan Academy 63,287 views

    Learn more: http://www.khanacademy.org/video?v=hrIPO8mQqtw
    Finding the volume when we have variable boundaries.

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    Double Integrals 6

    by Khan Academy 56,046 views

    Learn more: http://www.khanacademy.org/video?v=0pv0QtOi5l8
    Let's evaluate the double integrals with y=x^2 as one of the boundaries.

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    Triple Integrals 1

    by Khan Academy 111,880 views

    Learn more: http://www.khanacademy.org/video?v=vr0sTKbV7lI
    Introduction to the triple integral

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    Triple Integrals 2

    by Khan Academy 68,055 views

    Learn more: http://www.khanacademy.org/video?v=vxQvL_WhBGU
    Using a triple integral to find the mass of a volume of variable density.

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    Triple Integrals 3

    by Khan Academy 75,039 views

    Learn more: http://www.khanacademy.org/video?v=ZN2PfqZ4ihM
    Figuring out the boundaries of integration.

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    (2^ln x)/x Antiderivative Example

    by Khan Academy 57,032 views

    Learn more: http://www.khanacademy.org/video?v=C5Lbjbyr1t4
    Finding ∫(2^ln x)/x dx

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    Introduction to the Line Integral

    by Khan Academy 130,129 views

    Learn more: http://www.khanacademy.org/video?v=_60sKaoRmhU
    Introduction to the Line Integral

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    Line Integral Example 1

    by Khan Academy 92,080 views

    Learn more: http://www.khanacademy.org/video?v=uXjQ8yc9Pdg
    Concrete example using a line integral

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    Line Integral Example 2 (part 1)

    by Khan Academy 55,981 views

    Learn more: http://www.khanacademy.org/video?v=wyTjyQMVvc4
    Line integral over a closed path (part 1)

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    Line Integral Example 2 (part 2)

    by Khan Academy 35,313 views

    Learn more: http://www.khanacademy.org/video?v=Qqanbd3gLhw
    Part 2 of an example of taking a line integral over a closed path

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    Position Vector Valued Functions

    by Khan Academy 62,640 views

    Learn more: http://www.khanacademy.org/video?v=sBldw95xMD4
    Using a position vector valued function to describe a curve or path

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    Derivative of a position vector valued function

    by Khan Academy 44,406 views

    Learn more: http://www.khanacademy.org/video?v=E9Q_Lc0g1xE
    Visualizing the derivative of a position vector valued function

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    Differential of a vector valued function

    by Khan Academy 31,243 views

    Learn more: http://www.khanacademy.org/video?v=FYMn61HLw1k
    Understanding the differential of a vector valued function

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    Vector valued function derivative example

    by Khan Academy 32,793 views

    Learn more: http://www.khanacademy.org/video?v=vcwvzUVLPw0
    Concrete example of the derivative of a vector valued function to better understand what it means

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    Line Integrals and Vector Fields

    by Khan Academy 90,165 views

    Learn more: http://www.khanacademy.org/video?v=t3cJYNdQLYg
    Using line integrals to find the work done on a particle moving through a vector field

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    Using a line integral to find the work done by a vector field example

    by Khan Academy 68,384 views

    Learn more: http://www.khanacademy.org/video?v=AFF8FXxt5os
    Using a line integral to find the work done by a vector field example

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    Parametrization of a Reverse Path

    by Khan Academy 30,880 views

    Learn more: http://www.khanacademy.org/video?v=eGRZKkmI_fo
    Understanding how to parametrize a reverse path for the same curve.

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    Scalar Field Line Integral Independent of Path Direction

    by Khan Academy 29,948 views

    Learn more: http://www.khanacademy.org/video?v=99pD1-6ZpuM
    Showing that the line integral of a scalar field is independent of path direction

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    Vector Field Line Integrals Dependent on Path Direction

    by Khan Academy 35,619 views

    Learn more: http://www.khanacademy.org/video?v=fuSOY9r1R6w
    Showing that, unlike line integrals of scalar fields, line integrals over vector fields are path direction dependent

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    Path Independence for Line Integrals

    by Khan Academy 40,254 views

    Learn more: http://www.khanacademy.org/video?v=K_fgnCJOI8I
    Showing that if a vector field is the gradient of a scalar field, then its line integral is path independent

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    Closed Curve Line Integrals of Conservative Vector Fields

    by Khan Academy 34,526 views

    Learn more: http://www.khanacademy.org/video?v=I2dbzp0zHuw
    Showing that the line integral along closed curves of conservative vector fields is zero

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    Example of Closed Line Integral of Conservative Field

    by Khan Academy 24,865 views

    Learn more: http://www.khanacademy.org/video?v=Q9t1LghwdGc
    Example of taking a closed line integral of a conservative field

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    Second Example of Line Integral of Conservative Vector Field

    by Khan Academy 22,286 views

    Learn more: http://www.khanacademy.org/video?v=LpY8Qa3IP1w
    Using path independence of a conservative vector field to solve a line integral

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    Green's Theorem Proof Part 1

    by Khan Academy 74,684 views

    Learn more: http://www.khanacademy.org/video?v=l5zJvZKfMYE
    Part 1 of the proof of Green's Theorem

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    Green's Theorem Proof (part 2)

    by Khan Academy 35,029 views

    Learn more: http://www.khanacademy.org/video?v=qdFD-0OWBRo
    Part 2 of the proof of Green's Theorem

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    Green's Theorem Example 1

    by Khan Academy 77,422 views

    Learn more: http://www.khanacademy.org/video?v=gGXnILbrhsM
    Using Green's Theorem to solve a line integral of a vector field

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    Green's Theorem Example 2

    by Khan Academy 40,414 views

    Learn more: http://www.khanacademy.org/video?v=sSyPAAyL8nQ
    Another example applying Green's Theorem

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    Introduction to Parametrizing a Surface with Two Parameters

    by Khan Academy 54,891 views

    Learn more: http://www.khanacademy.org/video?v=owKAHXf1y1A
    Introduction to Parametrizing a Surface with Two Parameters

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    Determining a Position Vector-Valued Function for a Parametrization of Two Parameters

    by Khan Academy 29,456 views

    Learn more: http://www.khanacademy.org/video?v=bJ_09eoCmag
    Determining a Position Vector-Valued Function for a Parametrization of Two Parameters

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    Partial Derivatives of Vector-Valued Functions

    by Khan Academy 30,976 views

    Learn more: http://www.khanacademy.org/video?v=c7ByaI3T7Dc
    Partial Derivatives of Vector-Valued Functions

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    Introduction to the Surface Integral

    by Khan Academy 71,371 views

    Learn more: http://www.khanacademy.org/video?v=9k97m8oWnaY
    Introduction to the surface integral

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    Example of calculating a surface integral part 1

    by Khan Academy 47,318 views

    Example of calculating a surface integral part 1

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    Example of calculating a surface integral part 2

    by Khan Academy 20,452 views

    Learn more: http://www.khanacademy.org/video?v=qQAhhithHa8
    Example of calculating a surface integral part 2

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    Example of calculating a surface integral part 3

    by Khan Academy 23,006 views

    Learn more: http://www.khanacademy.org/video?v=s2_NTiISZl4
    Example of calculating a surface integral part 3

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    2011 Calculus AB Free Response #1a

    by Khan Academy 41,249 views

    Learn more: http://www.khanacademy.org/video?v=ppBJWf_Wdmc
    Determining whether speed is increasing. Difference between speed and acceleration

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    2011 Calculus AB Free Response #1 parts b c d

    by Khan Academy 20,861 views

    Learn more: http://www.khanacademy.org/video?v=QackTJWqOjA
    Integration to find average value of a function. Using a graphing calculator to calculate definite integrals.

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    2011 Calculus AB Free Response #2 (a & b)

    by Khan Academy 17,679 views

    Learn more: http://www.khanacademy.org/video?v=Z3X6QqezqUg
    Approximating rate of change and total area under a curve. Trapezoidal sums to approximate integrals

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    2011 Calculus AB Free Response #2 (c & d)

    by Khan Academy 13,093 views

    Learn more: http://www.khanacademy.org/video?v=2axaRJQkfVk
    Second fundamental theorem of calculus application

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    2011 Calculus AB Free Response #3 (a & b)

    by Khan Academy 12,297 views

    Learn more: http://www.khanacademy.org/video?v=9UhChwcVWq8
    Equation of a tangent line and area between curves

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    2011 Calculus AB Free Response #3 (c)

    by Khan Academy 9,635 views

    Learn more: http://www.khanacademy.org/video?v=v-H_7o7EMoU
    Disk method to find the volume of a solid generated by rotation of a function

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    2011 Calculus AB Free Response #4a

    by Khan Academy 11,759 views

    Learn more: http://www.khanacademy.org/video?v=tnoPnyvVjyc
    Taking derivatives and integrals of strangely defined functions

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    2011 Calculus AB Free Response #4b

    by Khan Academy 10,580 views

    Learn more: http://www.khanacademy.org/video?v=OvMBNVi5bLY
    Absolute maximum over an interval. Critical points and differentiability.

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    2011 Calculus AB Free Response #4c

    by Khan Academy 7,663 views

    Learn more: http://www.khanacademy.org/video?v=M_ADc9jkBig
    Finding the points of inflection for a strangely defined function

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    2011 Calculus AB Free Response #4d

    by Khan Academy 7,326 views

    Learn more: http://www.khanacademy.org/video?v=yX3JpmEgNHo
    Mean Value Theorem and differentiability

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    2011 Calculus AB Free Response #5a

    by Khan Academy 9,546 views

    Learn more: http://www.khanacademy.org/video?v=n9UvuzI2fq0
    Using a tangent line to extrapolate a function from a known initial condition

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    2011 Calculus AB Free Response #5b

    by Khan Academy 8,061 views

    Learn more: http://www.khanacademy.org/video?v=hAAIgNzBGg0
    Using the second derivative to judge whether an approximation with the tangent line is an overestimate or underestimate

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    2011 Calculus AB Free Response #5c.

    by Khan Academy 8,321 views

    Learn more: http://www.khanacademy.org/video?v=R-2Uw10QgIo
    Solving a differential equation using separation of variables

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    2011 Calculus AB Free Response #6a

    by Khan Academy 15,702 views

    Learn more: http://www.khanacademy.org/video?v=fr-8tjLoeDw
    Continuity of piecewise-defined functions

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    2011 Calculus AB Free Response #6b

    by Khan Academy 9,521 views

    Learn more: http://www.khanacademy.org/video?v=RuEJzPQ_N10
    Derivative of a piecewise-defined function

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    2011 Calculus AB Free Response #6c

    by Khan Academy 6,868 views

    Learn more: http://www.khanacademy.org/video?v=ucghWyc2_qs
    Average value of a piecewise-defined function on an interval

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    2011 Calculus BC Free Response #1a

    by Khan Academy 8,084 views

    Learn more: http://www.khanacademy.org/video?v=wtLTb_VaI-k
    Velocity and acceleration vectors for particle

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    2011 Calculus BC Free Response #1 (b & c)

    by Khan Academy 5,200 views

    Learn more: http://www.khanacademy.org/video?v=73eSiVcg4tQ
    Position and slope of particle's path at a given time

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    2011 Calculus BC Free Response #1d

    by Khan Academy 8,527 views

    Learn more: http://www.khanacademy.org/video?v=v-4QScXlN0o
    Arc length for a curve

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    2011 Calculus BC Free Response #3a

    by Khan Academy 6,493 views

    Learn more: http://www.khanacademy.org/video?v=_G9JwTwjulA
    Arc length of a function

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    2011 Calculus BC Free Response #3 (b & c)

    by Khan Academy 4,911 views

    Learn more: http://www.khanacademy.org/video?v=lpXCvX6ZenM
    Volume of a solid of rotation and Chain Rule for rates of change.

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    2011 Calculus BC Free Response #6a

    by Khan Academy 7,433 views

    Learn more: http://www.khanacademy.org/video?v=1BGlbx67B6s
    Taylor Series approximation of sin(x)

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    2011 Calculus BC Free Response #6b

    by Khan Academy 5,777 views

    Learn more: http://www.khanacademy.org/video?v=NQazgcu8c7s
    Taylor Series for cos x at x=0

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    2011 Calculus BC Free Response #6c

    by Khan Academy 7,017 views

    Learn more: http://www.khanacademy.org/video?v=l1hJABkcuYI
    Calculating the 6th derivative at 0 from the Taylor Series approximation

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    Error or Remainder of a Taylor Polynomial Approximation

    by Khan Academy 62,106 views

    Learn more: http://www.khanacademy.org/video?v=wgkRH5Uoavk
    Understanding the properties of the remainder or error function for an Nth degree Taylor approximation of a function

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    Proof: Bounding the Error or Remainder of a Taylor Polynomial Approximation

    by Khan Academy 44,183 views

    Learn more: http://www.khanacademy.org/video?v=yUUPP70Fhpo
    Proof of the Lagrange Error Bound (the bound of the error)

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    2011 Calculus BC Free Response #6d

    by Khan Academy 15,849 views

    Learn more: http://www.khanacademy.org/video?v=m6oMgtGsAa4
    Lagrange error bound for Taylor Polynomial approximation

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    Constructing a unit normal vector to a curve

    by Khan Academy 13,599 views

    Learn more: http://www.khanacademy.org/video?v=_9x2cqO7-Ig
    Figuring out a unit normal vector at any point along a curve defined by a position vector function

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    [Deleted Video]

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    2 D Divergence Theorem

    by Khan Academy 18,083 views

    Learn more: http://www.khanacademy.org/video?v=eoJGBr-tJXo
    Using Green's Theorem to establish a two dimensional version of the Divergence Theorem

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    Conceptual clarification for 2-D Divergence Theorem

    by Khan Academy 6,608 views

    Learn more: http://www.khanacademy.org/video?v=qs0hRHfnzTQ
    Understanding the line integral as flux through a boundary

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    Surface Integral Example Part 2 - Calculating the Surface Differential

    by Khan Academy 8,849 views

    Learn more: http://www.khanacademy.org/video?v=tyVCA_8MUV4
    Taking the cross product to calculate the surface differential in terms of the parameters

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    Surface Integral Example Part 1 - Parameterizing the Unit Sphere

    by Khan Academy 16,824 views

    Learn more: http://www.khanacademy.org/video?v=E_Hwhp74Rhc
    Visualizing a suitable parameterization

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    Surface Integral Example Part 3 - The Home Stretch

    by Khan Academy 7,245 views

    Learn more: http://www.khanacademy.org/video?v=uzOXGgAgmPs
    Using a few trigonometric identities to finally calculate the value of the surface integral

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    Surface Integral Ex2 part 1 - Parameterizing the Surface

    by Khan Academy 8,493 views

    Learn more: http://www.khanacademy.org/video?v=PpUWpxAb39w
    Parametrizing a surface that can be explictly made a function of x and y.

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    Surface Integral Ex2 part 2 - Evaluating Integral

    by Khan Academy 7,252 views

    Learn more: http://www.khanacademy.org/video?v=ItW5CxLsLSo
    Evaluating the surface integral

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    Surface Integral Ex3 part 1 - Parameterizing the Outside Surface

    by Khan Academy 7,129 views

    Learn more: http://www.khanacademy.org/video?v=EOpzN8ZHqpU
    Breaking apart a larger surface into its components

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    Surface Integral Ex3 part 2 - Evaluating the Outside Surface

    by Khan Academy 5,079 views

    Learn more: http://www.khanacademy.org/video?v=xGiILI906C4
    Evaluating the surface integral over the outside of the chopped cylinder

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    Surface Integral Ex3 part 3 - Top surface

    by Khan Academy 4,777 views

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