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I just can't figure out this problem. I would like to know how I can figure it out more than just the answer. The x's need to be canceled out to figure it out but I can't think of how to do that without an equation.


If $\lim\limits_{x\to0} \frac{f(x)}{x^2} = 9$, evaluate the following limits:

  • (a) $\lim\limits_{x\to0} f(x)$.

  • (b) $\lim\limits_{x\to0} \frac{f(x)}x$

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    What does the limit in the question mean? Essentially that $f(x) \sim 9x^2$ around $0$. From that, you can guess what the two other limits are. The rest is just a matter of formalizing the answers, if you need a proof.2011-10-16
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    Hint: the actual limit is meaningless, it is enough to know that the limit exists.2011-10-16
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    It is good practice to make the post self-contained, see http://meta.math.stackexchange.com/questions/2483/broken-imgur-links http://meta.math.stackexchange.com/questions/2674/how-self-contained-should-questions-be and other topics in meta linked to these ones. I've edited your post, you should check whether some further edits are needed.2011-10-16

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