Question

What is the oblique asymptote of the funtion -13x3-22x2-86x-50/x2+x+6?

Answer 1

\[\LARGE {-13x^3-22x^2-86x-50 \over x^2+x+6}\] this ?

Answer 2

yes

Answer 3

ok.. I'll ask you a simple question:
do you know how to find asymptotes?
how about this?
can you find obliques asymptote of this?
\[\LARGE f(x)={x^2\over x+2}\]
?

Answer 4

The only thing i know is you divide the domain so my first guess would be that i know the answer begins with x but the +2 confuses me.

Answer 5

Ok.. If I solve MY example, step by step, would you try to solve yours, following its steps ? :)

Answer 6

Yes, that would be helpful

Answer 7

ok...

Answer 8

so we have:
\[\LARGE f(x)={x^2 \over x+2 }\]
now we should use this equation:
\[\LARGE y=kx+b\quad \quad ,\quad k\neq 0\]
and we have:
\[\Large k=\lim_{x\to \infty}{f(x)\over x}\quad \quad \text{and}\quad \quad b=\lim_{x\to \infty} \left[{f(x)-kx}\right]\]

so
\[\Large k=\lim_{x\to \infty}{f(x)\over x}=\lim_{x\to \infty} \frac{\frac{x^2}{x+2}}{x}= \]
\[\Large =\lim_{x\to \infty} \frac{x^2}{x(x+2)}=\lim_{x\to \infty}\frac{x}{x\left(1+\frac2x\right)} =\]
\[\Large =\frac{1}{1+0}=1\]
so k=1

now we find b

\[\Large b=\lim_{x\to \infty}[f(x)-kx]=\lim_{x\to\infty}[\frac{x^2}{x+2}-1\cdot x]=\]
\[\Large =\lim_{x\to \infty}\left[\frac{\cancel{x^2}\cancel{-x^2}-2x}{x+2}\right]=...=-2\]
so b=-2

we substitute
y=kx+b
y=1*x-2
y=x-2

Answer 9

Oh wow. Thank you very much for your help. I think once I keep reviewing the help you have given me I will be able to figure the problem out.
I'm taking an online class and it's difficult without a teacher actually standing in front of you, but I think I'll understand it eventually lol. Thank you again.

Answer 10

My pleasure, I used a "simplier" function just to avoid big numbers, ;) Good Luck.

Answer 11

and remember one thing.
\[\LARGE k\neq 0\]
so.. when you'll be doing it, if you'll get k=0
don't continue any further. That's it. There's no oblique asymptote :)...
Take care my friend ...

Answer 12

Thank you (:

Answer 13

:)