Question: $\lim_{x \rightarrow 0}$ \|x\| <sup>sin x</sup> =...

Question

$\lim_{x \rightarrow 0}$ |x| ^{sin x} =

Answer 1

Let y = $\lim_{x \rightarrow 0}$ |x|^sinx 0⁰ form

log y = $\lim_{x \rightarrow 0}$ sin x log |x| 0 × a

log y = $\lim_{x \rightarrow 0}$ $\frac { \log | x | } { \operatorname { cosec } x }$ $\frac{\alpha}{\alpha}$

Apply L' Hospital rule

log y = $\lim _ { x \rightarrow 0 }$ $\frac{1/x}{\text{cosec x cot x}}$

log y = $\lim_{x \rightarrow 0}$ – $\left( \frac{\sin x}{x} \right)$ tan x

log y = 0

y = 1

Question: \(\lim_{x \rightarrow 0}\) \|x\| <sup>sin x</sup> =...