Question

Find the constant a, or the constants a and b, such that the function is continuous on the entire real line.

Answer 1

Step 1:

The function is

The function is continuous for all values of x.

For a limit to exists, the left hand limit is always equal to right hand limit.

.

 

Consider  .

Consider .

For a limit to exist, .

                (1).

Step 2:

For a limit to exists, the left hand limit is always equal to right hand limit.

.

 

Consider  .

Consider  .

For a limit to exist, .

           (2).

Step 3:

Find the values of a and b.

Subtract equation (2) from equation (1).

Substitute in equation (1).

The values are and  .

Solution:

The values are and .