1. ## Limit Problem

$\displaystyle \lim_{x \to 0} f(x)/x^2 = 6$

I'm supposed to find the limit of $\displaystyle f(x)$ and the limit of $\displaystyle f(x)/x$. (As $\displaystyle x$ approaches 0 in both cases)

I've looked through the entire section of my textbook and I don't see anything directly covering this question. Any hints?

2. Originally Posted by topher0805
$\displaystyle \lim_{x \to 0} f(x)/x^2 = 6$

I'm supposed to find the limit of $\displaystyle f(x)$ and the limit of $\displaystyle f(x)/x$. (As $\displaystyle x$ approaches 0 in both cases)

I've looked through the entire section of my textbook and I don't see anything directly covering this question. Any hints?
I hope you can see that $\displaystyle f(x) = 6x^2$ satisfies $\displaystyle \lim_{x \to 0} f(x)/x^2 = 6$. So, without any further information, as far as I'm concerned that's a perfectly good rule for f(x).

Then:

$\displaystyle \lim_{x \to 0} f(x) = \lim_{x \to 0} 6x^2 = 0$.

$\displaystyle \lim_{x \to 0} \frac{f(x)}{x} = \lim_{x \to 0} \frac{6x^2}{x} = \lim_{x \to 0} 6x = 0$.

Personally, I think the question is pretty dumb.

3. I agree, the question is dumb. When I first looked at it, my first inclination was to do what you did there, but it seemed like I was missing something. Thanks for the help.