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Math Help - Need help in limits for trigo

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by xcluded View Post
    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.
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