# Limits of Basic and Common Functions

The limits of two basic and common functions are are presented with examples and detailed solutions. Exercises are also included with their answers.

## Limits of Basic Functions

We present the limits of some basic functions.1. For f(x) = c , where c is a constant ,

2. For f(x) = x ,

## Examples with Detailed Solutions

### Example 1

Find the following limits.1. \( \lim_{x\to\ 6} (-2) \)

2. \( \lim_{x\to\ -\infty} (0) \)

3. \( \lim_{x\to\ +\infty} (x) \)

__Solutions to Example 1:__

1. The function is constant and equal to -2, we apply 1.a above, hence

\( \lim_{x\to\ 6} (-2) = -2 \)

2. The function is constant and equal to 0, we apply 1.c above, hence

\( \lim_{x\to\ -\infty} (0) = 0 \)

2. The function is equal to x, we apply 2.b above, hence

\( \lim_{x\to\ +\infty} (x) = +\infty \)

## Exercises

Find the following limits.1. \( \lim_{x\to\ -\infty} (6) \)

2. \( \lim_{x\to\ -5} (0) \)

3. \( \lim_{x\to\ -\infty} x \)

4. \( \lim_{x\to\ 1/2} (x) \)

### Answers to Above Exercises

1. \( \lim_{x\to\ -\infty} (6) = 6 \)2. \( \lim_{x\to\ -5} (0) = 0 \)

3. \( \lim_{x\to\ -\infty} x = -\infty \)

4. \( \lim_{x\to\ 1/2} (x) = 1/2 \)

## More References and links on Limits

Calculus Tutorials and ProblemsLimits of Absolute Value Functions Questions