# 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 LimitsCalculus Tutorials and Problems
Limits of Absolute Value Functions Questions |