The question asks to calculate the limit of the following function:
I'm struggling to figure out how to approach this? Should I approach it from the left hand side first of $-1$ and then the right hand side? It is hard to say since $x=-1$ is not included in the first expression.
When we talk about limit at $-1$, we don't look at what happens at $-1$, we look at what happens around $-1$, so the limit is just \begin{align*} \lim_{x\rightarrow -1}\dfrac{x^{4}-1}{x+1}&=\lim_{x\rightarrow -1}\dfrac{(x^{2}-1)(x^{2}+1)}{x+1}\\ &=\lim_{x\rightarrow -1}\dfrac{(x+1)(x-1)(x^{2}+1)}{x+1}\\ &=\lim_{x\rightarrow -1}(x-1)(x^{2}+1)\\ &=-4. \end{align*}