- #1

- 728

- 1

## Homework Statement

Find the first four non-vanishing terms of the Taylor series for xcotx in the neighborhood of x = 0.

## Homework Equations

## The Attempt at a Solution

LaTex isn't working for me so hopefully this doesn't look too messy.

cotx = cosx/sinx. I know what the Taylor series is for cosx and sinx about x = 0.

cosx = 1 - x^2/2! + x^4/4! + ..

sinx = x - x^3/3! + x^5/5! +...

so cotx = (1 - x^2/2! + x^4/4! + ..) / (x - x^3/3! + x^5/5! +...)

and so xcotx = (x - x^3/2! + x^5/4! + ..) / (x - x^3/3! + x^5/5! +...)

And so the first non-vanishing terms are:

1: x / (x - x^3/3! + x^5/5! +...)

2: -x^3/2! / (x - x^3/3! + x^5/5! +...)

and so on?

Is this right?