Step 1:

The function is  and .

Linear approximation of the function is .

Consider .

Differentiate on each side with respect to .

Substitute  in above function.

. \ \

. \ \

Substitute in the function.

. \ \

Linear approximation at  is .

Substitute all these values in linear approximation equation.

.

The corresponding linear approximation is .

Step 2:

Approximate value for . 

Here, .

.

Approximate value for .

Exact value of the .

The approximation is not good since the difference is more.

Approximate value for . 

.

Here, .

Approximate value for . \ \

Exact value of the .

The approximation is not good since the difference is large. \ \ \ \ \ \ Solution:

 Linear approximation of the function is  . \ \

Approximate value for .

Approximate value for .

The approximation is not good since the approximation values are differ from the exact values.

Graph of the function and the tangent is

.