- #1
knowlewj01
- 110
- 0
Homework Statement
find the limit of:
[itex]\frac{lim}{x\rightarrow0} ln(x)sin(x)[/itex]
tip:
you know that
[itex] \frac{sin(x)}{x} \rightarrow 1[/itex]
so rearrange to use
Homework Equations
L'hopitals rule?
The Attempt at a Solution
i rearranged to get this
[itex]\frac{lim}{x\rightarrow0} \frac{\frac{ln(x)sin(x)}{x}}{\frac{1}{x}}[/itex]
i know that [itex]\frac{sin(x)}{x} \rightarrow 1[/itex]
and [itex]\frac{1}{x} \rightarrow \infty[/itex]
does [itex]ln(x) \rightarrow -\infty[/itex] ?
I might need to use L'hopitals rule after this but i don't think it will make anything any easier.
Am i missing something major here, does the fact that sin(0)=0 mean that the limit is 0? because if it is, the question is fairly misleading.