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)
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