So I've got this limit:
$$\lim_{x\to 3^-} \frac{x^2-9}{|x-3|}$$
My (wrong) answer was zero. I figured that since the numerator approaches zero then regardless of what the denominator was, the whole function would approach zero. However, after looking at the graph I realize that this is not the case, the function approaches $-6$ when $x$ gets closer to $3$ (using values below than 3). How could one solve this without recurring to the graph?
Best Answer
you can factorize the numerator as $(x-3)(x+3)$.
Note that: $|x-3| = 3-x$ when $x$ goes to $3$ from the left hand side and cancel those two, and see what you will get.