Step 1:

The function .

Find the successive differentiation of .

.

Centered at .

Substitute .

.

Step 2:

Definition of Taylor series:

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

is called Taylor series for at .

Substitute the above values in Taylor series.

.

.

The Taylor series for centered at is .

Solution:

The Taylor series for centered at is ..

(2)

Step 1:

The function .

Find the successive differentiation of .

.

Centered at .

Substitute in .

.

Step 2:

Definition of Taylor series:

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

is called Taylor series for at .

\

Substitute the above values in Taylor series.

.

The Taylor series for centered at is .

Solution:

\

The Taylor series for centered at is .