- #1

lo2

- 55

- 0

## Homework Statement

I have this function:

[itex]f(x) = \frac{1}{x}-\frac{\cos{(x)}}{\sin{(x)}}[/itex]

For all [itex]x \in R[/itex] where [itex] x \neq n \pi, n \in Z [/itex]

Ok I have to find the following limit:

[itex]lim_{x\rightarrow0+}(f(x))[/itex]

## Homework Equations

Limits in general and perhaps the always great Hospital's rule.

## The Attempt at a Solution

I have tried to put on the same fraction line:

[itex]f(x) = \frac{\sin{(x)}-x\cos{(x)}}{x\sin{(x)}}[/itex]

And then using the Hospital rule, but it does not really seem to bring me any further...

The first derivative of it is:

[itex]f(x) = \frac{x^2-1+(\cos{(x)})^2}{x^2(\sin{(x)})^2}[/itex]

And then I could use the Hospital rule again but it just seems as though it will make it worse, the sinus will always be in the denominator.