Asymptote of the

Question

x^2/(x^2+9)?

Answer 1

To find the  vertical asymptote ,set denominator equal to zero and solve.

x^2+9=0

x^2=-9

No solution for this equation.

Therefore, the vertical asymptote is none.

Calculate the  horizontal asymptote ,

lim         x^2/(x^2+9)

x---> ∞

 

lim         x^2/x^2(1+9/x^2)

x---> ∞

Cancel common terms

 

im         1/(1+9/x^2)

x---> ∞

=1

Therefore, the horizontal asymptote is y=1.