TITLE: A couple of questions about limits
QUESTION [7 upvotes]: I'm doing some homework for a calculus course I am taking and, though I feel silly because I've done problems like this before, I'm having some issues. I feel like I am getting the wrong answers for a couple of problems, and I'd like a second (or third, or tenth) opinion.
1) Find $\lim_{x\to 1}f(x)$ where: $$f(x) = \left\{ 
 \begin{array}{cc} 
     x^2+2, & x\neq 1\\ 
     1, & x=1 \end{array} \right.$$
I'm thinking that the limit does not exist, since you have to plug 1 in to the equation, making x=1, meaning f(x) =1. Please, correct me if I'm wrong.
2) $\lim_{x\to -1} \frac{x^3-1}{x+1}$
I said it is undefined, but I'm not sure...

REPLY [3 votes]: For the $2$ problem the as $x \to -1$ $f(x) = \displaystyle\frac{x^{3}-1}{x+1} \to -\infty$. Here is the graph