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 FunctionsWe present the limits of some basic functions. 1. For f(x) = c where c is a constant ,
2. For f(x) = x,
Example 1: Find the following limits.
\lim_{x\to\ 6} (-2)
2.
\lim_{x\to\ -\infty} (0)
3.
\lim_{x\to\ +\infty} (x)
Solutions to Example 1:
\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.
\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:
\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
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