# 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 Problems
Limits of Absolute Value Functions Questions