Math Help - Need help in limits for trigo

1. Need help in limits for trigo

Hi everyone. I'm very poor in maths. I have been cracking my head over this question for half of the day , to no avail.

Lim x-> 0+ , Cot x / ln x

= lim x-> 0+ (- csc^2 x / 1/x) (By L'H)

= - lim x-> 0+ (x . 1/sin^2 x)

I'm stuck after there. Did I wrote wrongly there?

Thanks

2. Originally Posted by xcluded
Hi everyone. I'm very poor in maths. I have been cracking my head over this question for half of the day , to no avail.

Lim x-> 0+ , Cot x / ln x

= lim x-> 0+ (- csc^2 x / 1/x) (By L'H)

= - lim x-> 0+ (x . 1/sin^2 x)

I'm stuck after there. Did I wrote wrongly there?

Thanks
You have

$- \lim_{x \rightarrow 0^+} \frac{x}{\sin x} \cdot \lim_{x \rightarrow 0^+} \frac{1}{\sin x} = -1 \cdot \lim_{x \rightarrow 0^+} \frac{1}{\sin x} = - \infty$.