lim-x-0-1-x-2-cot-2-x-

Question Number 155120 by mnjuly1970 last updated on 25/Sep/21

{l i m}_{x \to 0} (\frac{1}{x^{2}} - {c o t}^{2} (x)) = ?

Answered by john_santu last updated on 25/Sep/21

\lim_{x \to 0} (\frac{1}{x^{2}} - \cot^{2} x) = \lim_{x \to 0} (\frac{1}{x^{2}} - \frac{1}{\tan^{2} x})

= \lim_{x \to 0} (\frac{\tan x + x}{\tan x}) \times \lim_{x \to 0} (\frac{\tan x - x}{x^{2} \tan x})

= 2 \times \frac{1}{3} = \frac{2}{3}

Commented by mnjuly1970 last updated on 25/Sep/21

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