hi everyone!

needed some help on two questions.

1. Find the first 3 non-zero terms in the series for

2. Assuming the series for and , determine the series for up to and including the term in

thank you.

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- Jan 30th 2007, 12:56 PMEnitaseries
hi everyone!

needed some help on two questions.

1. Find the first 3 non-zero terms in the series for

2. Assuming the series for and , determine the series for up to and including the term in

thank you. - Jan 30th 2007, 02:15 PMCaptainBlack
Well we need the Taylor series about 0.

So lets look at the sequence of derivatives and find the first three which are non-zero.

First the zero-th drrivative is non-zeros at and equal to

The first derivative:

which is zero at

Second derivative:

which is equal to at

Third derivative:

which is zero at

Fourth derivative:

which is when .

So the series expansion of to the first three non zero terms is:

so (if I have done this right):

RonL - Jan 31st 2007, 12:41 PMEnita
- Jan 31st 2007, 01:04 PMCaptainBlack