Is it possible to evaluate this limit without series expansion and l'Hôpital's rule?

Asked Jun 13 '12 at 16:19

Active Jun 13 '12 at 16:22

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Limits without l'Hôpital

I have a limit which is to be evaluated without using l'Hôpital's rule or series expansion. $$ \lim_{x \rightarrow 0}\frac{\frac{\sin x}{x} - \cos x}{2x \left ( \frac{e^{2x} - 1}{2x} - 1 \right ) }$$ Is it possible to evaluate it without l'Hôpital's rule or series expansion only using trigonometric and algebraic manipulation?

edited Apr 13 '17 at 12:20

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asked Jun 13 '12 at 16:19

S L

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i think this is a duplicate . – Theorem Jun 13 '12 at 16:21
can you send the link?? ... to the original ... i'll delete the question – S L Jun 13 '12 at 16:22
Lol ... you are right ... i sounded like 'lopital' ... though they taught L hospital ... in school ... lol :D – S L Jun 13 '12 at 16:25
how do i eliminate those e's?? – S L Jun 13 '12 at 17:09
Lol ... when did he ask??? he never told me – S L Jun 13 '12 at 21:34
i would still like to know it ... without expanding ... if it's possible – S L Jun 13 '12 at 21:38

Is it possible to evaluate this limit without series expansion and l'Hôpital's rule?

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