Question

I'm trying to factor this equation in order to find its limit, but I'm not sure how to go about it. I can get the answer by graphing on a calculator but I need to do it without one.

Function:
F(x)=(x^2-36)/(sqrt(x^2-12x+36))
left, right, and overall lim as it approaches 6

Answer 1

let's look at that bottom part
√(x^2 - 12x + 36)
= √(x-6)^2
= x-6

so you have
f(x) = (x-6)(x+6)/x-6)
= x+6

so as x --> 6
limit f(x) = 12