# Limits of Basic Functions

The limits of two basic functions are are presented with examples and detailed solutions.

## Limits of Basic Functions

We present the limits of some basic functions.

1. For f(x) = c where c is a constant ,

• a. limx→ a f(x) = c

• b. limx→ +∞f(x) = c

• c. limx→ -∞f(x) = c

2. For f(x) = x,

• a. limx→a f(x) = a

• b. limx→+∞ f(x) = +∞

• c. limx→-∞ f(x) = -∞

Example 1: Find the following limits.

1. limx→6 ( -2 )

2. limx→-∞ ( 0 )

3. limx→+∞ (x)

Solutions to Example 1:

1. The function is constant and equal to -2, we apply 1.a above, hence

limx→6 ( -2 ) = -2

2. The function is constant and equal to 0, we apply 1.c above, hence

limx→-∞ ( 0 ) = 0

2. The function is equal to x, we apply 2.b above, hence

limx→+∞ x = +∞

Exercises: Find the following limits.

1. limx→-∞ ( 6 )

2. limx→-5 ( 0 )

3. limx→-∞ (x)

4. limx→(1/2) (x)

Solutions to Above Exercises:

1. limx→-∞ ( 6 ) = 6

2. limx→-5 ( 0 ) = 0

3. limx→-∞ x = -∞

4. limx→(1/2) x = (1/2)

More on limits

Calculus Tutorials and Problems