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.
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