Solving Limits and Discontinuities: f(x)= 3x2-12x / x2-6x +8

[Econometricia]

1. f(x)= 3x²-12x / x²-6x +8



f(x) can be made continuous at x =4 by defining f(4)=6

I know that the removable disc. is at x=2 and the non removable is at x=4. So there is an asymptote at x=4. How is it possible to define it there?

 

[Dick]

You have that backwards. There's no asymptote at x=4. There's an asymptote at x=2. Find the limit as x->4. Show your work this time.

 

[Econometricia]

Ugh! Thanks I am just a fool and factored incorrectly. Final exams =(. Thank you !

3x(x-4) / (x-4)(x-2) = f(x)
So the lim as x-->4 f(x)=6