Answer
$$ \infty$$
Work Step by Step
Given
$$\lim _{x \rightarrow -\infty}\frac{1+x^6}{x^4+1}$$
Then
\begin{aligned}
\lim _{x \rightarrow -\infty}\frac{1+x^6}{x^4+1}&=\lim _{x \rightarrow -\infty}\frac{1/x^4+x^6/x^4}{x^4/x^4+1/x^4} \\
&=\frac{\lim _{x \rightarrow -\infty}(1/x^4)+\lim _{x \rightarrow -\infty}(x^2)}{\lim _{x \rightarrow -\infty}(1)+\lim _{x \rightarrow -\infty}(1/x^4)}\\
&=\lim _{x \rightarrow -\infty}(x^2)\\
&= \infty
\end{aligned}
