Mathematics - Limits Question with Solution | TestHub

$\underset{x\to 0^{+}}{\mathrm{Lt}}(\sqrt{\tan x}{)}^{\sqrt{x}}+\underset{x\to 0^{+}}{\mathrm{Lt}}(\cos x{)}^{-1/x}$

$e^{{\mathrm{Lt}}_{x\to 0^{+}}\frac{{\log }_e(\sqrt{\tan x})}{\frac{1}{\sqrt{x}}}\left(\frac{-\infty }{\infty }\right)=e^0=1,{\mathrm{Lt}}_{x\to 0^{+}}(\cos x{)}^{-1/x}=1\text{ as }0<\cos x<1}$