L'Hospital's Rule

Practice Questions

GRE Subject Test: Math › L'Hospital's Rule

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1

Evaluate the limit using L'Hopital's Rule.

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

2

Evaluate the following limit

$\small \lim_{x\to 0} \frac{\cos x-(x-1)^2}{x^3-3x}$

if possible.

3

Find the limit if it exists

$\lim_{x\rightarrow 0}\frac{sin(x)-x}{x^2}$

Hint: Use L'Hospital's rule

4

Evaluate the following limit:

$\lim_{x\rightarrow 3} \frac{3-x}{x^2-9}$

5

Use l'Hopital's rule to find the limit:

$\lim_{x \to 1} \frac{x^2-3x+2}{x-1}$

6

Determine the limit of:

$\lim_{n\to \infty} \left(\frac{n+1}{n}\right)^2$

7

Evaluate the limit:

$\lim_{x\rightarrow 9}\frac{\cos(\frac{\pi}{2}+9-x)}{\ln(x-8)}$

8

Evaluate the following limit:

$\lim_{x\rightarrow 2}\frac{x^2-4}{\sin(2-x)}$

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

Evaluate the limit:

$\lim_{x\rightarrow 5}\frac{x^2-25}{\sin(x-5)}$

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