Calculate the following limits: \text { a) } \lim _{x \rightarrow \infty}\left(\frac{5 x+2}{x-1}\right) \text { b) } \lim _{x \rightarrow \infty}\left(\frac{x^{2}+3 x}{x^{2}-5}\right) \text { c) } \lim _{x \rightarrow a}\left(\frac{x^{n}-a^{n}}{x-a}\right)

\text { d) } \lim _{x \rightarrow 3}\left(\frac{x-3}{\sqrt{x-2}-\sqrt{4-x}}\right) \text { e) } \lim _{x \rightarrow 2}\left(\frac{3 x^{3}-11 x^{2}-2 x+24}{6 x^{3}-13 x^{2}-13 x+30}\right)