Derivatives

Practice Questions

AP Calculus BC › Derivatives

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1

Evaluate the limit using L'Hopital's Rule.

$\lim_{x\rightarrow \infty }\frac{x^2}{e^x+1}$

2

$g(x) = e ^{x^{2}+x}$

Evaluate .

3

$g(x) = e ^{x^{2}+x}$

Evaluate .

4

$g(x) = e ^{x^{2}+x}$

Evaluate .

5

$\begin{align*}&\text{The expression of a particular function is unknown;}\&\text{however, we have an expression for its derivative.}\&\text{Knowing that }f'(x)=4e^{(2x)}\text{ and }f(0)=9\&\text{Approximate } f(4.8)\text{ using Euler's Method and }4\text{ steps.}\end{align*}$

6

Evaluate the limit using L'Hopital's Rule.

$\lim_{x\rightarrow \infty }\frac{x^2}{e^x+1}$

7

$\begin{align*}&\text{The expression of a particular function is unknown;}\&\text{however, we have an expression for its derivative.}\&\text{Knowing that }f'(x)=4e^{(2x)}\text{ and }f(0)=9\&\text{Approximate } f(4.8)\text{ using Euler's Method and }4\text{ steps.}\end{align*}$

8

Evaluate the limit using L'Hopital's Rule.

$\lim_{x\rightarrow \infty }\frac{x^2}{e^x+1}$

9

$\begin{align*}&\text{The expression of a particular function is unknown;}\&\text{however, we have an expression for its derivative.}\&\text{Knowing that }f'(x)=4e^{(2x)}\text{ and }f(0)=9\&\text{Approximate } f(4.8)\text{ using Euler's Method and }4\text{ steps.}\end{align*}$

10

Let on the interval $(0,\frac{\pi}{2})$ . Find a value for the number(s) that satisfies the mean value theorem for this function and interval.

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