# 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 ,
• a.
\lim_{x\to\ a} f(x) = c

• b.
\lim_{x\to\ +\infty} f(x) = c

• c.
\lim_{x\to\ -\infty} f(x) = c

2. For f(x) = x,

• a.
\lim_{x\to\ a} f(x) = a

• b.
\lim_{x\to\ +\infty} f(x) = +\infty

• c.
\lim_{x\to\ -\infty} f(x) = -\infty

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)

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

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