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Question Number 188771 by mnjuly1970 last updated on 06/Mar/23

Commented by mahdipoor last updated on 06/Mar/23

$$lim(x\to 0^{+})\sqrt{cos\left(\sqrt{cos\left(x\right)}\right)}=\sqrt{cos\left(1\right)}=a$$$$\Rightarrow 0<a<\frac{1}{2}\stackrel{b>0}{\Rightarrow }{0}^b<a^b<1^b\Rightarrow 0<a^b<\frac{1}{2^b}$$$$\Rightarrow b=cot\left(x\right)\to +\mathrm{\infty }\Rightarrow 0<a^b<0\Rightarrow$$$$limit=0$$

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