Calculus AB Review of Limits, Derivatives, and Integrals

Question 1

\lim_{x	o0}\frac{x^2+5x}{e^x-1}=

Accepted Answer

5

Question 2

An integral finds the area under and/or above the curve of a function

Accepted Answer

True

Question 3

f'\left(xight)=\lim_{h	o0}\frac{f\left(x+hight)-f\left(xight)}{h}

Accepted Answer

True

Question 4

\int_{ }^{ }x^2dx=

Accepted Answer

\frac{1}{3}x^3+C

Question 5

A derivative tells us...

Accepted Answer

The instantaneous rate of change of a function, The slope at a point on a function, The slope of a tangent line to a function

Question 6

\frac{d}{dx}\left(4x^2\cos x\right)=

Accepted Answer

-4x^2\sin x+8x\cos x

Question 7

Find \frac{dy}{dx} when y=\sin^{-1}\left(\frac{1}{x}\right)

Accepted Answer

\frac{dy}{dx}=-\frac{1}{x^2\sqrt{1-\frac{1}{x^2}}}

Question 8

\int_{ }^{ }-\frac{1}{x^2\sqrt{1-(\frac{1}{x})^2}}dx

Accepted Answer

\arcsin\left(\frac{1}{x}\right)+C

Question 9

\int_1^e\frac{1}{x}dx=

Accepted Answer

1

Question 10

\int_1^2\left(8x^3+6x^2-5x\right)dx

Accepted Answer

\frac{73}{2}

Question 11

\lim_{h	o0}\frac{\frac{1}{\left(x+hight)^3}-\frac{1}{x^3}}{h}=

Accepted Answer

-\frac{3}{x^4}, -\frac{3x^2}{x^6}

Question 12

\frac{d}{dx}\left(2\cos\left(4x^2+9x-6\right)^2\right)=

Accepted Answer

-2\cos\left(4x^2+9x-6\right)\sin\left(4x^2-9x+6\right)\left(8x+9\right)

Question 13

Which is not a condition of continuity of a function?

Accepted Answer

\lim_{x	o c}f\left(cight)=f\left(xight)

Questions 13