# Power Series expansion of hyperbolic functions

1. Feb 1, 2009

### thanksie037

1. The problem statement, all variables and given/known data

power series expansion of:

((cosh x)/(sinh x)) - (1/x)

2. Relevant equations

cosh x = (1/2)(ex + e-x)
sinh x = (1/2)(ex - e-x)

3. The attempt at a solution
what i have so far:

I simplified the first part of the eq to read :
e2x-1
e2x-1

2. Feb 1, 2009

### NoMoreExams

You simplified for it to be $$\frac{e^{2x}-1}{e^{2x}-1}$$? Isn't that just 1?

3. Feb 1, 2009

### mjsd

error in simplification:

$$\frac{e^{2x}+1}{e^{2x}-1}$$

4. Feb 1, 2009

### thanksie037

I'm sorry that was a typo. Should I just expand both was like you would ex? how about the 1/x part?

5. Feb 1, 2009

### NoMoreExams

I would and then hopefully things will cancel, for example what's the expansion for $$e^{2x} - 1$$?

6. Feb 2, 2009

### mjsd

How do one usually find the taylor series of a given function?
now you have a function, what do you do?