Find the Limit of a Function

Practice Questions

Pre-Calculus › Find the Limit of a Function

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1

Calculate $\lim_{x\rightarrow \infty }\left ( x^{2} \sin \frac{1}{ x^{2}-1} - \sin \frac{1}{ x^{2}-1} \right )$ .

2

Find the limit

$\lim_{x\rightarrow \frac{3}{2}}\frac{6x^2-5x-6}{2x-3}$

3

Find the limit as x approaches infinity

$\lim_{x\rightarrow \infty }\frac{3x^3-5x^4+4}{14x^2+32x^3}$

4

Finding limits of rational functions.

Let

$f(x)=\frac{x^{2}-9}{x+3}$ .

Find

$\lim_{x\rightarrow -3}f(x)$ .

5

Solve the following limit:

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

6

Evaluate the following limit.

$\lim_{x\rightarrow 0}\frac{x^2+3x}{3x^2+4x}$

7

Let $f(x)=\frac{x+7}{x^{2}-2}$ .

Find $\lim_{x\rightarrow 2}$ .

8

The speed of a car traveling on the highway is given by the following function of time:

What can you say about the car's speed after a long time (that is, as approaches infinity)?

9

Solve the limit as approaches infinity.

$\lim_{x\rightarrow \infty }\frac{3x^4-2^7x^2+4x}{5x^2-13x^4+5x}$

10

Find the limit of the function:

$\lim_{x\rightarrow 5^{+}} \frac{5}{5-x}$

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