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

1 Answer
Nov 5, 2016

Answer:

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#