Cracking The Ap Calculus ab Exam 2018

not, and recall that v(t) = x′(t) and a(t) = x′′(t). First, take the derivative of x(t), set it equa ...

Now, plug into the equation above to get 17.321 = −10(−5) and ≈ 2.887 C = . At t = . A ...

ANSWERS AND EXPLANATIONS TO SECTION II Water is dripping from a pipe into a container whose volume ...

The volume of water in the container can be found by integrating the new expression for from part (b): ...

Let R be the region enclosed by the graphs of y = , y = x^2 , and the lines x = 0 and x = 1. ...

(2x^2 + 8y) = − 3x^2 − 4xy (b) Find the equation of the tangent line to the curve at x = 0. First ...

plug in the rate the volume is changing, = 64π, and the radius given, 20 in. , so 64π ...

To determine the equation of the ball’s height, repeat the procedure in part (a), but integrate the velocity ...

Appendix ...

DERIVATIVES AND INTEGRALS THAT YOU SHOULD KNOW [ku] = k [k] = 0 [uv] = u + v 4. [eu] = eu [ln u] ...

[sin−1 u] = [tan−1 u] = [sec−1 u] = 1.∫ k du = ku + C 2.∫ un du = + C; n ≠ − 1 3.∫ ...

13.∫ sec u tan u du = sec u + C 14.∫ csc u cot u du = − csc u + C 15.∫ + C; |u| < a 16. = ...

When you raise an expression to the power of zero, you get one. x^0 = 1 When you raise an expression t ...

are logs with base e and are denoted by ln. Thus, you should know the following: ln 1 = 0 ln e = 1 l ...

sin θ = csc θ = Thus, sin θ = cos θ = sec θ = Thus, cos θ = tan θ = cot θ = T ...

sin 0 = 0 cos 0 = 1 tan 0 = 0 sin cos tan sin cos tan = 1 sin cos tan sin = ...

About the Author David S. Kahn studied applied mathematics and physics at the University of Wisconsin and has taug ...

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