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help? linear approximations?

0 votes

asked May 6, 2015 in CALCULUS by anonymous

1 Answer

0 votes

4)

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 the corresponding values in linear approximation equation.

.

The corresponding linear approximation is image.

answered May 6, 2015 by cameron Mentor
edited May 6, 2015 by cameron

Continued....

Step 2:

Approximate value for image

image

Here, image.

image

image

image.

Approximate value for image.

Exact value of the image.

The approximation is not good since the difference between approximation and exact value is more.

Approximate value for image

image

Here, image.

image

image

image

Approximate value for image.

Exact value of the image.

The approximation is not good since the difference between approximation and exact value 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.

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