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 ,
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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