Question

Use the definition of continuity and the properties of limits to show that the function is continuous on the given interval.

f (x) = (2x +3)/(x - 2),        (2, ∞)

Answer 1

Step 1:

The function is and interval .

Definition of Continuity:

A function is  continuous at a number , if .

If then by using limits law,

Properties of limits: .

Hence, .

Step 2:

Consider different values of which lies in the interval .

	3	5	7	10
	9	4.33	3.40	2.875

Observe the table.

The function is  continuous at for every in the interval .

Solution  :

The function is continuous on the interval .