1. ## l'Hospital's Rule

Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. If l'Hospital's Rule doesn't apply, explain why.

lim as x -> o+ (sinxlnx)

I got the equation to be zero, but now I am unsure on whether l'Hospital's Rule is appropriate and how to show this.

Any help would be very much appreciated, thanks.

2. Originally Posted by Amybee
Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. If l'Hospital's Rule doesn't apply, explain why.

lim as x -> o+ (sinxlnx)

I got the equation to be zero, but now I am unsure on whether l'Hospital's Rule is appropriate and how to show this.

Any help would be very much appreciated, thanks.

L'H rule is appliable here since both functions $\displaystyle \ln x\,,\,\,\frac{1}{\sin x}$ are derivable in a right neighborhood of zero, we get an indeterminate of the form $\displaystyle \frac{\infty}{\infty}$ and the limit $\displaystyle \lim_{x\to 0}\frac{(\ln x)'}{\left(\frac{1}{\sin x}\right)'}$ exists and it's finite (it's zero)

Tonio