Step 1:

The function is  and the value of is .

Linearization of the function is at is  .

Consider .

Differentiate on each side with respect to .

.

Derivative of the logarithmic function: .

.

.

Substitute in above function.

.

.

Step 2:

Linearization of the function is at is .

Substitute corresponding values in linear approximation equation.

.

Solution:

Linear approximation to the function at the point is .

2)

Step 1:

The function is  and the value of is .

Linearization of the function is at is  .

Consider .

Differentiate on each side with respect to .

.

Derivative of the logarithmic function: .

.

Substitute in above function.

.

.

.

Step 2:

Linearization of the function is at is .

Substitute corresponding values in linear approximation equation.

.

Solution:

Linear approximation to the function at the point is .

3)

Step 1:

The function is  and the value of is .

Linearization of the function is at is  .

Consider .

Differentiate on each side with respect to .

.

.

Power rule of derivatives: .

.

Substitute in above function.

.

.

Substitute in above function.

.

Step 2:

Linearization of the function is at is .

Substitute corresponding values in linear approximation equation.

.

Solution:

Linear approximation to the function at the point is .