Question

Let \(\Large f(x) = \dfrac{2x^3+4x^2-9}{x-3}\) and s(x) be the slant asymptote of f. Find the value of s(-2).

How can I find the slant asymptote?

Answer 1

Is s(x) supposed to be linear function or can it be quadratic function?

Answer 2

I think you are supposed to divide the top by the bottom first.

Answer 3

\[
\lim_{x\to \infty }|f(x) - L| = 0
\]

Answer 4

This is what I did and I got 2x²+10x+30. I ignored remainder because it is unnecessary.

Answer 5

Does it work on this formula?

Answer 6

What is that?

Answer 7

Definition of slant asymptote

Answer 8

Never seen this formula... what does L represent?

Answer 9

Where L is the expression of the slant asymptote.

Answer 10

Sorry, I don't get it. I rather solve it algebraically.

Answer 11

s(x) = 2x²+10x+30 right?

Answer 12

Yes.

Answer 13

So s(-2) = 8-20+30 = \(\boxed{18}\).