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