(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

What is the value of

lim {(1/x)^{sinx}+(sinx)^{1/x}} ,x>0 ???

x->0

2. Relevant equations

??

3. The attempt at a solution

lim {(1/x)^{sinx}+(sinx)^{1/x}}

x->0

=lim (1/x)^{sinx}+lim (sinx)^{1/x}

..x->0............x->0

Let A=lim (1/x)^{sinx}

.........x->0

and B=lim (sinx)^{1/x}

.........x->0

logA=lim (sinx)log(1/x)=0

........x->0

=>A=e^{0}=1

logB=lim (1/x)log(sinx)=infinity

........x->0

=>B=infinity

The problem is that the answer is 0.

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# Homework Help: Limit of the form 0^infinity+infinity^0

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