## Calculus (3rd Edition)

The left and right limits are equal when $n$ is even.
Consider the case when $n$ is even (e.g. $1/x^2$), \begin{align*} \lim _{x \rightarrow 0-} \frac{1}{x^{n}}&=\infty\\ \lim _{x \rightarrow 0+} \frac{1}{x^{n}}&=\infty \end{align*} and for $n$ is odd (e.g. $1/x^3$), \begin{align*} \lim _{x \rightarrow 0-} \frac{1}{x^{n}}&=-\infty\\ \lim _{x \rightarrow 0+} \frac{1}{x^{n}}&=\infty \end{align*} We see that the left and right limits are equal for even powers of $n$, but not for odd powers.