frosty8688 said:
1.Find the asymptotes of the following equation.
2. \left.x/(x-1)^2\right.
To be an equation, there needs to be an = somewhere.
frosty8688 said:
3. I know that the asymptote as x approaches ±∞ is ±∞.
?
As x gets large or very negative, the denominator of x/(x - 1)
2 is much larger than the numerator.
frosty8688 said:
I am wondering when (x-1)^{2} approaches ±∞ is also ±∞
Now I think I know what you're trying to say. You seem to be using "asymptote" in place of "limit." The two words are not synonyms, and don't mean the same thing.
As x approaches ∞, both x and (x - 1)
2 approach ∞. As x approaches -∞, x approaches -∞, but (x - 1)
2 approaches +∞. Another way to say this is
$$\lim_{x \to -\infty} (x - 1)^2 = \infty $$
The thing is, the denominator gets large much more quickly than the numerator. One way to approach this problem is to factor x
2 out of each term in the denominator, and factor x
2 out of the numerator.
