- #1

Jarfi

- 384

- 12

**Struggling with this limit value**

## Homework Statement

Calculate lim((e^x-1)/x)^(1/sin(x)) where x[itex]\rightarrow0[/itex]

## Homework Equations

Maclaurin series.

sin(x)/x -----> 1 when x->0 (possibly)

## The Attempt at a Solution

(e^x-1)/x)^(1/sin(x) = ((x+x^2/2+x^3H(x))/x)^(1/sin(x)) =((1+x/2+x^2H(x))/x)^(1/sin(x))

Then getting something like:

1+(1/sinx)C(1)*(1+x/2+x^2H(x))/x) + (1+x/2+x^2H(x))/x)^2*(1/sinx)C(2)

which results in total chaos.

Anybody have a SIMPLE solution?

p.s sorry for the lack of readability, writing math in Physicsforums is a F-ing pain. I mean what the H is [it0ex]\rightharp0oonup[/it0ex] and [itex0]\frac{}{0}[/itex0] telling me.

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