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Question Number 91020 by jagoll last updated on 27/Apr/20

$$\underset{x\to 0}{\lim }{\left(\sin x\right)}^{\frac{1}{x}}?$$

Commented by jagoll last updated on 28/Apr/20

$$itdoesmean\underset{x\to 0}{\lim }{\left(\sin x\right)}^{\frac{1}{x}}DNE?$$

Commented by mathmax by abdo last updated on 27/Apr/20

$$letf\left(x\right)={\left(sinx\right)}^{\frac{1}{x}}\Rightarrow f\left(x\right)=e^{\frac{1}{x}ln\left(sinx\right)}$$$$\frac{ln\left(sinx\right)}{x}\sim \frac{ln\left(x\right)}{x}\to -\mathrm{\infty }(x\to 0^{+})\Rightarrow {lim}_{x\to 0^{+}}f\left(x\right)=0$$

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