Question

Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a.

f (x) = (x + 2x³ )⁴ ,     a = - 1

Answer 1

Step 1:

The function is , .

A function is continuous at , if then it should satisfy three conditions :

(1) is defined.

(2) exists.

(3) .

Step 2:

(1)

Substitute in the above expression.

is defined.

(2)

exists.

(3)

and

.

From above the three conditions are satisfied.

Hence, the function is continuous.

Solution :

The function is continuous at .