# Thread: Find the slant asymptote?

1. ## Find the slant asymptote?

(x^3-4x²+2x-5)/(x²+2)

2. Originally Posted by puzzledwithpolynomials
Find the slant asymptote?

(x^3-4x²+2x-5)/(x²+2)
do the long division ... the quotient will be a linear expression that is the equation of the slant asymptote (ignore the remainder).

here's a link with some examples ...

Slant, or Oblique, Asymptotes

3. Did you figure out the answer? I learned about oblique/slant asymptotes a week ago and I thought I might try this problem out for practice. Would the answer by any chance be : x-4 R 4x+3 OR x-4 + (4x+3/x^2-2) Oblique asymptote being x-4 . Not sure If I am allowed to supply answers but I would just like to see if I am right.

Sean

4. Originally Posted by SeanBE
Did you figure out the answer? I learned about oblique/slant asymptotes a week ago and I thought I might try this problem out for practice. Would the answer by any chance be : x-4 R 4x+3 OR x-4 + (4x+3/x^2-2) Oblique asymptote being x-4 . Not sure If I am allowed to supply answers but I would just like to see if I am right.

Sean
quotient is ...

$\displaystyle x - 4 + \frac{3}{x^2+2}$

slant asymptote is $\displaystyle y = x - 4$

5. A slant asymptote always has this form:

y=mx+n

Where :

$\displaystyle m=\lim_{x\rightarrow\inf}\frac{f(x)}{x}$

and

$\displaystyle n=\lim_{x\rightarrow\inf}(f(x)-mx)$

In this particular case of yours you have :

$\displaystyle m=\lim_{x\rightarrow\inf}\frac{\frac{x^3-4x^2+2x-5}{x^2+2}}{x}=\lim_{x\rightarrow\inf}\frac{x^3-4x^2+2x-5}{x^3+2x} = 1$

$\displaystyle n=\lim_{x\rightarrow\inf}(\frac{x^3-4x^2+2x-5}{x^2+2}-x)=\lim_{x\rightarrow\inf}\frac{-4x^2-5}{x^2+2}=-4$

So the fianl result will be :

$\displaystyle y=mx+n=1*x-4 =x-4$

That's all,

Have a nice day!