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Question #51d9b

1 Answer

Dec 26, 2017

$lim_{x->0^+}(sin2x)^(x^(-2))=0$

Explanation:

$lim_{x->0^+}(sin2x)^(x^(-2))=lim_{x->0^+}(sin2x)^(1/x^2)=$

$lim_{x->0^+}e^(1/x^2*ln(sin2x))$

Let's calculate this limit now :

$lim_{x->0^+}ln(sin2x)*1/x^2=-oo$

So now our limit becomes:

$lim_{u->-oo}e^u=0$

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