$$\displaystyle \frac{20^2$}{2 \times 9.8}$$ meters

Question 1

Which of the following is the correct result for $$\displaystyle \frac{x^7$}{x^3$}$$?

Accepted Answer

$$x^4$$

Question 2

If $$f(x) = x^2$ and g(x$$) = \sin(x)$$, what is the derivative of h(x) = f(x$$) \cdot g(x)$$ using the product rule?

Accepted Answer

$$2x \sin(x) + x^2$ \cos(x)$$

Question 3

Evaluate the limit: $$\displaystyle \lim_{x 	o 0} \frac{\sin(x)}{x}.$$

Accepted Answer

$$1$$

Question 4

Which of the following is the correct application of the chain rule for $$\displaystyle \frac{d}{dx} \left( \sin(x^2$) \right)$$?

Accepted Answer

$$2x \cos(x^2$)$$

Question 5

A ball is thrown upward with velocity $$v(t) = 20 - 9.8t. $$What is the maximum height reached by the ball?

Accepted Answer

$$\displaystyle \frac{20^2$}{2 	imes 9.8}$$ meters

Question 6

Which of the following is the correct simplification for $$\displaystyle (x^3$)^4$?

Accepted Answer

$$x^{12}$$

Question 7

Find the derivative of $$f(x) = \ln(x^2$ + 1).$$

Accepted Answer

$$\displaystyle \frac{2x}{x^2$ + 1}$$

Question 8

Which of the following is the correct result for $$x^0$$ when $$x 
eq 0$$?

Accepted Answer

$$1$$

Question 9

If $$\displaystyle \lim_{x 	o a} f(x) = L$$ and $$\displaystyle \lim_{x 	o a} g(x) = M$$, what is $$\displaystyle \lim_{x 	o a} [f(x) + g(x)]$$?

Accepted Answer

$$L + M$$

Question 10

Which of the following is the correct simplification for $$\displaystyle \frac{1}{x$$^{-3}$$}$$?

Accepted Answer

$$x^3$$

Question 11

A population of bacteria grows according to $$P(t) = P_0$ e$$^{kt}$$. If the population doubles in 3 hours, what is the value of k$?

Accepted Answer

$$\displaystyle \frac{\ln 2}{3}$$

Question 12

Which of the following is the correct result for $$\displaystyle \frac{d}{dx} (e$$^{2x}$$)$$?

Accepted Answer

$$2e^{2x}$$

Question 13

Which of the following is the correct simplification for $$\displaystyle \frac{x^5$}{x^8$}$$?

Accepted Answer

$$x^{-3}$$

Question 14

If $$f(x) = x^2$ and g(x$$) = $$x^3$$, what is $$f(g(x))$$?

Accepted Answer

$$(x^3)^2$ = x^6$

Question 15

Which of the following is the correct result for $$\displaystyle \frac{d}{dx} (\cos(x))$$?

Accepted Answer

$$-\sin(x)$$

Question 16

A car's position is given by $$s(t) = 4t^2$ + 2t + 1. $$What is its velocity at $$t = 3$$ seconds?

Accepted Answer

$$26$$

Question 17

Which of the following is the correct simplification for $$\displaystyle (x^2$ y^3$)^4$?

Accepted Answer

$$x^8$$ $$y^{12}$$

Question 18

Which of the following is the correct result for $$\displaystyle \frac{d}{dx} (\ln(x))$$?

Accepted Answer

$$\displaystyle \frac{1}{x}$$

Question 19

If $$\displaystyle \lim_{x 	o 2} \frac{x^2$ - 4}{x - 2} is $$evaluated, what is the result?

Accepted Answer

$$2$$

Calculus Study Notes: Functions, Limits, and Pre-Calculus Foundations

Study Guide - Practice Questions