How do you find the slant asymptote of y=(x^3)/((x^2)-3)?
1 Answer
Aug 14, 2018
The slant asymptote is:
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