Find \(\lim_{x\to0^+}\frac{1}{x}\).

Find \(\lim_{x\to0^-}\frac{1}{x}\).

Find the one-sided limits of \(f(x)=\frac{1}{x-2}\) as \(x\to2\).

Evaluate \(\lim_{x\to3}\frac{1}{(x-3)^2}\).

Find \(\lim_{x\to1^+}\frac{x+2}{x-1}\).

Find \(\lim_{x\to1^-}\frac{x+2}{x-1}\).

Determine whether \(\lim_{x\to0}\frac{1}{x}\) exists as a two-sided infinite limit.

Find the one-sided limits of \(f(x)=\frac{x}{x^2-4}\) as \(x\to2\).

Find \(\lim_{x\to-2^+}\frac{x}{x^2-4}\).

For \(f(x)=\frac{2x-1}{(x+1)^2}\), find the infinite limit as \(x\to-1\).