Question

for $x>0;{lim}_{x\to 0}\left(\right(\sin x{)}^{\frac{1}{x}}+{\left(\frac{1}{x}\right)}^{\sin x})=$

• A. $0$
• B. $-1$
• C. $1$
• D. $2$

Answer 1

The correct option is A $0$

$\underset{x\to 0}{lt}({\left(sinx\right)}^{1/x}+{\left(1/x\right)}^{sinx})$

$=\underset{x\to 0}{lt}{\left(sinx\right)}^{1/x}+\underset{x\to 0}{lt}{\left(\frac{1}{x}\right)}^{sinx}=0$