Could one-sided limits not exist but not equal to $\pm\infty$

e.g. $\displaystyle \lim_{x->c^+}f(x)$ DNE and $\displaystyle \lim_{x->c^+}f(x)\neq\pm\infty$

  • $\begingroup$ Consider $x \mapsto \cos(\frac{1}{x})$. Obviously if the right-handed and left-handed limits as $x \rightarrow 0$ existed, they would be equal, because the function is even. $\endgroup$ – Jannik Pitt Mar 31 '18 at 15:09


Consider the function $$f(x)= \sin(1/x)$$ on the interval $(0,1).$

$$ \lim_{x\to {0^+}} f(x)$$ does not exist due to oscillations and the function is bounded.

  • 1
    $\begingroup$ You can use "\sin" instead of just "sin" (same for "lim"), then it won't appear italic. $\endgroup$ – Jannik Pitt Mar 31 '18 at 15:15
  • $\begingroup$ Thanks for the comment. I have edited my post per your advice. $\endgroup$ – Mohammad Riazi-Kermani Mar 31 '18 at 15:29

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