LIMITS, HELP PLEASE !!

[ilovemath]

A certain rational function f(x) contains quadratic functions in both its numberator and denominator. Aside from that, we also know the following things about f:
- F has a vertical asymptote at x=-6
- F has a single x-intercept of x=2
- F is removably discontinuous at x=3 since limxgoes to 3 f(x)=13/18

Based on these delightful clues, evaluate:
1. f(0)
2. Lim as x goes to infinity, f(x)

 

[Deleted member 4993]

A certain rational function f(x) contains quadratic functions in both its numberator and denominator. Aside from that, we also know the following things about f:
- F has a vertical asymptote at x=-6
- F has a single x-intercept of x=2
- F is removably discontinuous at x=3 since limxgoes to 3 f(x)=13/18

Based on these delightful clues, evaluate:
1. f(0)
2. Lim as x goes to infinity, f(x)

Well - start with:

\(\displaystyle f(x) \, = \, \frac{Ax^2 + Bx + C}{Dx^2 + Ex + F}\)

Please show us your work, including exactly where you are stuck - so that we know where to begin to help you