2. Compute each of the following limits. \( \begin{array}{lll}\text { a) } \lim _{x \rightarrow \infty} \frac{1}{x} & \text { d) } \lim _{x \rightarrow-\infty}\left(\frac{-5}{2 x^{3}}-7+\frac{8}{x}\right) & \text { g) } \lim _{x \rightarrow \infty} \frac{-5 x^{3}-2 x+4}{x^{2}} \\ \text { b) } \lim _{x \rightarrow-\infty} \frac{1}{x} & \text { e) } \lim _{x \rightarrow \infty}\left(-2 x^{3}+1-\frac{5}{x}+\frac{12}{x^{4}}\right) & \text { h) } \lim _{x \rightarrow \infty} \frac{-5 x^{3}-2 x+4}{x^{3}} \\ \text { c) } \lim _{x \rightarrow \infty} \frac{-5}{2 x^{3}} & \text { f) } \lim _{x \rightarrow-\infty} \frac{3 x-2}{x} & \text { i) } \lim _{x \rightarrow \infty} \frac{-5 x^{3}-2 x+4}{x^{4}}\end{array} \)

Let's compute the limits one by one: a) \(\lim _{x \rightarrow \infty} \frac{1}{x} = 0\) b) \(\lim _{x \rightarrow -\infty} \frac{1}{x} = 0\) c) \(\lim _{x \rightarrow \infty} \frac{-5}{2 x^{3}} = 0\) d) \(\lim _{x \rightarrow -\infty}\left(\frac{-5}{2 x^{3}}-7+\frac{8}{x}\right) = -7\) e) \(\lim _{x \rightarrow \infty}\left(-2 x^{3}+1-\frac{5}{x}+\frac{12}{x^{4}}\right) = -\infty\) f) \(\lim _{x \rightarrow -\infty} \frac{3 x-2}{x} = 3\) g) \(\lim _{x \rightarrow \infty} \frac{-5 x^{3}-2 x+4}{x^{2}} = -\infty\) h) \(\lim _{x \rightarrow \infty} \frac{-5 x^{3}-2 x+4}{x^{3}} = -5\) i) \(\lim _{x \rightarrow \infty} \frac{-5 x^{3}-2 x+4}{x^{4}} = 0\) In conclusion, each of these limits gives a different insight into the behavior of the functions as \( x \) approaches infinity or negative infinity!