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. lim_{x→ a} f(x) = c

b. lim_{x→ +∞}f(x) = c

c. lim_{x→ ∞}f(x) = c
2. For f(x) = x,

a. lim_{x→a} f(x) = a

b. lim_{x→+∞} f(x) = +∞

c. lim_{x→∞} f(x) = ∞
Example 1: Find the following limits.
1. lim_{x→6} ( 2 )
2. lim_{x→∞} ( 0 )
3. lim_{x→+∞} (x)
Solutions to Example 1:
1. The function is constant and equal to 2, we apply 1.a above, hence
lim_{x→6} ( 2 ) = 2
2. The function is constant and equal to 0, we apply 1.c above, hence
lim_{x→∞} ( 0 ) = 0
2. The function is equal to x, we apply 2.b above, hence
lim_{x→+∞} x = +∞
Exercises: Find the following limits.
1. lim_{x→∞} ( 6 )
2. lim_{x→5} ( 0 )
3. lim_{x→∞} (x)
4. lim_{x→(1/2)} (x)
Solutions to Above Exercises:
1. lim_{x→∞} ( 6 ) = 6
2. lim_{x→5} ( 0 ) = 0
3. lim_{x→∞} x = ∞
4. lim_{x→(1/2)} x = (1/2)
More on limits
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