I'm working on Proofs for Limits. So my question is how the bloody hell do I do this.

Question

This is the equation I am working with:
F(x)= (x^2-5x+8)(x-3)/(x-3)
Use the limit properties to prove algebraically that limf(x)=2 as X approaches 3

Answer 1

I would find the lim x>3^-, and the lim x>3⁺, and show that they are both 2. If they are equal, then
Lim x>3 is 2

Do this by inserting an (x+e) or (x-e) for x, where e is an arbritrary small number that can vanish. In both cases, you will have a e/e in the function, which divides to 1.

Answer 2

I've got a graph. It shows Limf(x) is two, There is some long way thanks though.