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

$$ f(x) = \begin{cases} \frac{1-\cos(5x)}{x^2} & x > 0 \\ \\ \frac{e^x + 2x -2}{x} & x < 0 \end{cases} $$

Find the limits for $x\rightarrow 0^-$ and for $x\rightarrow 0^+$.

Thanks in advance for any help!

share|cite|improve this question
Do you know what it means $x\rightarrow 0^-$ and $x\rightarrow 0^{+}$? – Mhenni Benghorbal Dec 22 '12 at 20:38
up vote 1 down vote accepted

Hints: $$\lim_{x\to 0^+}\frac{1-\cos 5x}{x^2}=\lim_{u\to 0^+}\frac{1-\cos u}{(\frac u 5)^2}$$ while $$\lim_{x\to 0^-}\frac{e^x+2x-2}{x}$$ is not indeterminate.

share|cite|improve this answer

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.