Quandaries & Queries - Math Central

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joseph, a student:

I am trying to find the limit as X approaches 0 from the positive side of x to the sin of x

which look like this lim x^sinx
x->0+

Hi Joseph,

Let y = x^sin(x) then ln(y) = ln(x^sin(x)) = sin(x) ln(x). If you can show that the limit of sin(x) ln(x) = a as x approaches zero from the right then the limit of x^sin(x) is e^a as x approaches zero from the right. I used l'Hopital's rule to evaluate the limit of sin(x) ln(x) as x approaches zero from the right.

Harley

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