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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