# Thread: show that f is continuous at -3

1. ## show that f is continuous at -3

Define f:[-4,0]->R by f(x)=2 $x^2$-18/x+3 for x $\neq$-3 and f(-3)= -12. Show that f is continuous at -3.

At first I was going to try to show that the lim_(x->-3)= -12 and I was going to reduce and stuff but im getting lost because its not working out smoothly. Also, can I just go ahead and show that (with help) or do I have to show a proof of it?

2. Sorry I kept thinking the denominator was x-3...So in the case, if I show the 2x^2-18/x+3 =(2x-6) and that the lim_(x->-3) 2x-6=-12 is that all i have to do to show that f is continuous at -3? since the lim as x->-3 of f(x)=f(-3)? Or again do I have to show a proof?