Suppose fx x 2 x 2 9 Determine an equation of the horizont

Suppose f(x) = x 2 x 2 9 . Determine an equation of the horizontal asymptote. Explain.

Solution

f(x) = (x 2)/(x² 9)

horizontal asymptote

y =lim_x->(x 2)/(x² 9)

y =lim_x->x(1 (2/x))/(x²(1 9/x²))

y =lim_x->(1 (2/x))/(x(1 9/x²))

y =(1 (0))/((1 0))

y=1/

y=0

y =lim_x->-(x 2)/(x² 9)

y =lim_x->-x(1 (2/x))/(x²(1 9/x²))

y =lim_x->-(1 (2/x))/(x(1 9/x²))

y =(1 (0))/(-(1 0))

y=-1/

y=0

only horizontal asymptote is y=0