Question

The value of $Li{m}_{x\to 0^{+}}(1/x{)}^{sinx}=?$

• A. $-1$
• B. $0$
• C. $1$
• D. $2$

Answer 1

Answer: (C)

$1$

Let $k=L{t}_{x\to 0^{+}}(1/x{)}^{sinx}$

$\Rightarrow \log k=L{t}_{x\to 0^{+}}\sin x\log \left(\frac{1}{x}\right)$
$\Rightarrow k=e^{-L{t}_{x\to 0^{+}}\sin x\log x}$
$\Rightarrow k=e^0=1$