Compute each of the following limits if they exist.

Question

lim 3x^(2)-x-2
x->2

lim (x^(2)+x-6)/(x-2)
x->2

Answer 1

#1: easy, since polynomials are continuous. f(2) = 8, which is the limit

#2:
x^2+x-6 = (x+3)(x-2)

so, f(x) = x+3 everywhere except at x=2. There it is undefined, but the limit is 5 from both sides.