use epsilon delta to prove the following

Question

lim x^2-9/x+3 =-6
x->-3

Answer 1

f(x) = (x^2-9)/(x+3) = (x-3)

Obviously the function is -6 when x = -3. You don't need to prove it with epsilons.

If you want to use epsilon, which I will call e, let x = -3 + e

f(x) = (9 -6e +e^2 -9)/e
= -6 +e
= -6 as e-> 0