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Could you give me some suggestions on how to solve these limits?

$\lim_{x \to 0} $ \frac{1}{x^2} - \frac{\cot x}{x} $$

$\lim_{ x \to -2} \[ \frac{1}{x+2} - \frac{1}{\ln(x+3)} \]$

$\lim_{x \to 1} \[ \frac{x-2}{2(x-1)^2} + \frac{1}{(x+1)(e^{2x-2} - 1)} \]$

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