${lim}_{x \to o} (\frac{1}{x^{2}} - c o t x)$

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Solution

$\begin{matrix} W e h a v e {lim}_{x \to 0} \frac{1}{x^{2}} - cot x = \frac{tan x - x^{2}}{x^{2} tan x} = \frac{{sec}^{2} x - 2 x}{2 x tan x - x^{2} {sec}^{2} x} = \frac{1 - 0}{0 + 0} = \frac{1}{0} = \infty (N o t d e f i n e d .) \end{matrix}$

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