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)


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