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 ,
formula of limits for a constant function
2. For
f(x) = x ,
formula of limits of 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