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