Question-203471

Question Number 203471 by DEGWE last updated on 19/Jan/24

Answered by MathematicalUser2357 last updated on 20/Jan/24

= \frac{\lim_{x \to 0^{+}} x^{cosec x + \cot x}}{\lim_{x \to 0^{+}} (cosec x + \cot x)}

= \frac{\lim_{x \to 0^{+}} x^{\frac{1}{\sin x} + \frac{1}{\tan x}}}{\lim_{x \to 0^{+}} (\frac{1}{\sin x} + \frac{1}{\tan x})}

= \frac{\lim_{x \to 0^{+}} x^{\frac{1 + \frac{\sin x}{\tan x}}{\sin x}}}{\lim_{x \to 0^{+}} \frac{1 + \frac{\sin x}{\tan x}}{\sin x}}

= \frac{\lim_{x \to 0^{+}} x^{\frac{1 + \cos x}{\sin x}}}{\lim_{x \to 0^{+}} \frac{1 + \cos x}{\sin x}}

= \frac{0}{1}

= 0