1. ## Continuous functions

Hi

The question is "find the value of k for each of the following functions that make them continueous everywhere"

F(x) = (2x^2-x-15)/(x-3) if x<3

and

F(x) = kx-1 if x >=3

What I don't understand is how you solve this if

lim f(x) = lim (2x^2-x-15)/(x-3) does not exist since you can't
x->3- x->3-

divide by zero.

I have six calculus books I am looking through and I can't find a single example of this. Any enlightenment would be greatly appreciated.

But if you let $g(x)=2x^2-x-15$, you can see that $g(3)=0$
thus (x-3) is a factor of $2x^2-x-15$
more precisely, $2x^2-x-15=(x-3)(2x-5)$