Determine the Following Limits, If They Exist $\lim _{x \rightarrow-2} x(x-2)^{2}$

Essay

Determine the following limits, if they exist.
(a) $\lim _{x \rightarrow-2} x(x-2)^{2}$
(b) $\lim _{x \rightarrow 3} \frac{x^{2}-7 x+12}{x^{2}-4 x+3}$
(c) $\lim _{x \rightarrow \infty} 5 x-2$
(d) $\lim _{x \rightarrow 0} \frac{\sin 5 x}{x^{2}-x}$
(e) $\lim _{x \rightarrow 3} \frac{x-3}{x^{2}+5}$
(f) $\lim _{x \rightarrow 0} \frac{2}{x}$