Question

How do you find the Vertical, Horizontal, and Oblique Asymptote given `g(x)=(2+x)/(x^2(5-x))`?

Answer 1

The vertical asymptotes are `x=0` and `x=5`
The horizontal asymptote is `y=0`

Explanation:

As we cannot divide by `0`, so `x!=0` and `x!=5`
`:. x=0` and `x=5` are vertical asymptotes
Rewrite the expression
`g(x)=(2/x+1)/(5x-x^2)=(2/x+1)/(x^2(5/x-1))`

limit `g(x)=0`
`x->-oo`

limit `g(x)=0^-`
`x->+oo`