- #1

doktorwho

- 181

- 6

## Homework Statement

##\frac{e^x-1}{x}##

Evaluate the limit of the expression as x approaches 0.

## Homework Equations

3. The Attempt at a Solution [/B]

The question i have is more theoretical. I was able to solve this problem by expanding the expression into the talyor polynomial at ##x=0##. I found that to be the easiest way to get to solution if tou asked to find a limit as x approaches 0. But my question is this:

If x approaches some constant could i do the same thing except evaluate at ##x=a##? And what about if x goes to infinity?

For example ##\frac{sinx}{x}## ##=0## as x goes to inifnity but when you try the expansion it doesnt. We can't then do that, so what would then be the easiest way?