taylor series?

Question

Answer 1

(1)

Step 1:

The function is .

Find the successive derivatives 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.

.

.

Solution:

The Taylor series is .

Answer 2

(2)

Step 1:

The function .

Find the successive derivatives 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.

.

.

Solution:

The Taylor series is .