Determine the Following Limits, If They Exist $\lim _{x \rightarrow 4} x(x+4)^{2}$

Essay

Determine the following limits, if they exist.
(a) $\lim _{x \rightarrow 4} x(x+4)^{2}$
(b) $\lim _{x \rightarrow 1} \frac{x^{2}+3 x-4}{x^{2}-6 x+5}$
(c) $\lim _{x \rightarrow-\infty} 6 x+2$
(d) $\lim _{x \rightarrow 0} \frac{\sin 5 x}{x}$
(e) $\lim _{x \rightarrow 4} \frac{x-4}{x^{2}+2}$
(f) $\lim _{x \rightarrow 0} \frac{2}{x^{2}}$