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## 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 dont 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.