91Ó°ÊÓ

Either find the given limit or show it does not exist. If the limit is infinite, indicate whether it is \(+\infty\) or \(-\infty\). $$ \lim _{x \rightarrow 0^{-}}\left(x^{3}-\frac{1}{x^{2}}\right) $$

Either find the given limit or show it does not exist. If the limit is infinite, indicate whether it is \(+\infty\) or \(-\infty\). $$ \lim _{x \rightarrow-\infty} \frac{x^{4}+3 x^{2}-2 x+7}{x^{3}+x+1} $$

Either find the given limit or show it does not exist. If the limit is infinite, indicate whether it is \(+\infty\) or \(-\infty\). $$ \lim _{x \rightarrow-\infty} \frac{x^{3}-3 x+5}{2 x+3} $$

Either find the given limit or show it does not exist. If the limit is infinite, indicate whether it is \(+\infty\) or \(-\infty\). $$ \lim _{x \rightarrow-\infty} \frac{x x^{2}}{x^{2}+3 x-1} $$

Either find the given limit or show it does not exist. If the limit is infinite, indicate whether it is \(+\infty\) or \(-\infty\). $$ \lim _{x \rightarrow-\infty} \frac{x(x-3)}{7-x^{2}} $$

Either find the given limit or show it does not exist. If the limit is infinite, indicate whether it is \(+\infty\) or \(-\infty\). $$ \lim _{x \rightarrow 0^{-}} x \sqrt{1-\frac{1}{x}} $$

Either find the given limit or show it does not exist. If the limit is infinite, indicate whether it is \(+\infty\) or \(-\infty\). $$ \lim _{x \rightarrow 0^{+}} \sqrt{x}\left(1+\frac{1}{x^{2}}\right) $$

List all values of \(x\) for which the given function is not continuous. f(x)=\frac{x^{2}-1}{x+3}

List all values of \(x\) for which the given function is not continuous. $$ f(x)=5 x^{3}-3 x+\sqrt{x} $$

List all values of \(x\) for which the given function is not continuous. $$ g(x)=\frac{x^{3}+5 x}{(x-2)(2 x+3)} $$