determine the limit without using L'Hospital – math.stackexchange.com

determine the limit without using L'Hospital – math.stackexchange.com

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How to prove that $$\lim\limits_{x\to 0, x\neq 0}\frac{e^{\sin(x)}-1}{\sin(2x)}=\frac{1}{2}$$ without using L'Hospital? Using L'Hospital, it's quite easy. But without, I don't get this. I tried ...

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