- #1

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- Homework Statement
- Consider ##f(x)=\frac{(a-2)x^3+x^2}{ax^2+6x+1}##:

for which values of ##a## has it an horizontal asymptote?

- Relevant Equations
- none

I'll write my procedure:

$$\lim_{x\to\infty}[\frac{(a-2)x^3+x^2}{ax^2+6x+1}]\rightarrow\frac{x(a-2)}{a}\in \mathbb{R}$$

And now, assumed that everything's correct, how do I assign ##a## a value for having that limit finite and ##\in \mathbb{R}##, and so an horizontal asymptote?

$$\lim_{x\to\infty}[\frac{(a-2)x^3+x^2}{ax^2+6x+1}]\rightarrow\frac{x(a-2)}{a}\in \mathbb{R}$$

And now, assumed that everything's correct, how do I assign ##a## a value for having that limit finite and ##\in \mathbb{R}##, and so an horizontal asymptote?