Applications of Derivatives

Practice Questions

AP Calculus BC › Applications of 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

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

3

Evaluate the limit using L'Hopital's Rule.

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

4

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

5

$\begin{align*}&\text{The expression of a particular function is unknown;}\&\text{however, we have an expression for its derivative.}\&\text{Knowing that }f'(x)=13tan(5x)\text{ and }f(2)=9\&\text{Approximate } f(11.9)\text{ using Euler's Method and }3\text{ steps.}\end{align*}$

6

$\begin{align*}&\text{The expression of a particular function is unknown;}\&\text{however, we have an expression for its derivative.}\&\text{Knowing that }f'(x)=13tan(5x)\text{ and }f(2)=9\&\text{Approximate } f(11.9)\text{ using Euler's Method and }3\text{ steps.}\end{align*}$

7

Find the

$\small \small \small \lim_{x\rightarrow 0}\frac{e^{x^{2}}-ln(1+x)-1}{cosx-sinx-1}$ .

8

Find the limit if it exists

$\lim_{x\rightarrow\infty }\frac{x^2+3x}{2+x^2}$

Hint: Use L'Hospital's rule

9

Find the limit if it exists

$\lim_{x\rightarrow\infty }\frac{x^2+3x}{2+x^2}$

Hint: Use L'Hospital's rule

10

Find the

$\small \small \small \lim_{x\rightarrow 0}\frac{e^{x^{2}}-ln(1+x)-1}{cosx-sinx-1}$ .

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