How do you find the slant asymptote of #y=(x^3)/((x^2)-3)#?

1 Answer
Aug 14, 2018

Answer:

The slant asymptote is: #y=x#

Explanation:

Given:

#y = x^3/(x^2-3)#

Note that:

#x^3/(x^2-3) = (x^3-3x+3x)/(x^2-3)#

#color(white)(x^3/(x^2-3)) = (x(x^2-3)+3x)/(x^2-3)#

#color(white)(x^3/(x^2-3)) = x+(3x)/(x^2-3)#

and:

#lim_(x->+-oo) (3x)/(x^2-3) = lim_(x->+-oo) 3/(x-3/x) = lim_(x->+-oo)3/x = 0#

So:

#y = x^3/(x^2-3)#

is asymptotic to #y=x#