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limx→0 (((1 + sinx)cotx −e)cotx).

 Apr 23, 2020
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I am not good at presenting these but I'll show you what I would do.

 

\(\displaystyle\lim_{x→0} (((1 + sinx)cotx −e)cotx)\\ =\displaystyle \lim_{x→0} \left[ \left[ (1 + 0)\frac{cosx}{sinx} −e\right]\frac{cosx}{sinx}\right]\\ =\displaystyle \lim_{x→0} \left[ \left[\frac{cosx}{sinx} −e\right]\frac{cosx}{sinx}\right]\\ \\~\\ \rightarrow+\infty\)

 

 

Maybe Heureka or someone some other mathematician may like to tidy up my presentation.

 Apr 23, 2020

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