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Math Help - l'Hospital's Rule

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by Amybee View Post
    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 \ln x\,,\,\,\frac{1}{\sin x} are derivable in a right neighborhood of zero, we get an indeterminate of the form \frac{\infty}{\infty} and the limit \lim_{x\to 0}\frac{(\ln x)'}{\left(\frac{1}{\sin x}\right)'} exists and it's finite (it's zero)

    Tonio
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