Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I need to find an example of a function $f(x)$ , that satisfies: $ \lim _ {x\to 0} \frac{f(x)}{x^2} = 5 $ , but $\lim _ {x \to 0 } f(x) $ doesn't exist.

Does someone have an idea?

Thanks in advance !

share|cite|improve this question
Such a function $f$ does not exist. Could you prove it? – Did Nov 12 '12 at 16:45
up vote 1 down vote accepted

Hint $\ $ Take the limit as $\rm\:x\to 0\:$ of $\rm\: f(x)\, =\, x^2 \dfrac{f(x)}{x^2}\ $ using the limit product rule.

share|cite|improve this answer
Thanks a lot !! there was indeed a mistake in the question's formulation – joshua Nov 12 '12 at 17:12

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.