The function is and , , .

(a)

Find the Taylor polynomial with degree  at the number .

Definition of Taylor series:

If a function  has derivatives of all orders at  then the series

 is called Taylor series for  at .

First find the successive derivatives of .

Apply derivative on each side with respect to .

Find the values of the above functions at .

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.

.

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The series is centered at .

Taylor series centered at .

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.

(b)

The taylors inequality is where  .

Here , and .

Substitute in

.

.

.

Substitute in .

.

The Taylors accuracy inequality is .

(c)

The value is .

Here .

Substitute and .

.

Graph :

Graph the function .

Observe the graph:

The functions for small value of in the interval .

(a) ..

(b) .

(c)

Graph of the function is

The functions for small value of in the interval .