Question Number 188771 by mnjuly1970 last updated on 06/Mar/23
Commented by mahdipoor last updated on 06/Mar/23
$${lim}\:\left({x}\rightarrow\mathrm{0}^{+} \right)\:\:\:\:\:\:\sqrt{{cos}\left(\sqrt{{cos}\left({x}\right)}\right)}=\sqrt{{cos}\left(\mathrm{1}\right)}={a} \\ $$$$\Rightarrow\mathrm{0}<{a}<\frac{\mathrm{1}}{\mathrm{2}}\overset{{b}>\mathrm{0}} {\Rightarrow}\mathrm{0}^{{b}} <{a}^{{b}} <\mathrm{1}^{{b}} \Rightarrow\mathrm{0}<{a}^{{b}} <\frac{\mathrm{1}}{\mathrm{2}^{{b}} } \\ $$$$\Rightarrow{b}={cot}\left({x}\right)\rightarrow+\infty\Rightarrow\mathrm{0}<{a}^{{b}} <\mathrm{0}\Rightarrow \\ $$$${limit}=\mathrm{0} \\ $$