0
$\begingroup$

I want to show a function $f$ such that $\displaystyle\lim_{x\to x_0}f(x^2)\in\mathbb{R}$ but $\displaystyle\lim_{x\to x_0}f(x)$ doesn't exist.

I only need a suggest of such a function $f$. I can't find an example of this.

Any hint? Thanks.

$\endgroup$
  • 3
    $\begingroup$ take any function $f(x)$ that is continuous at $x=x_0^2$ and has a jump at $x = x_0$ $\endgroup$ – Petite Etincelle Oct 17 '14 at 13:31
  • $\begingroup$ And if $x_o$ is infinite :)? $\endgroup$ – mvggz Oct 17 '14 at 13:32
6
$\begingroup$

Let $f(x) = \begin{cases} -1,&x < 0,\\1,& x \geq 0, \end{cases}$ with $x_0 = 0$.

$\endgroup$
  • $\begingroup$ You're welcome. $\endgroup$ – fuglede Oct 17 '14 at 13:51

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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