Using several times L'Hospital Rule I got $$\lim_{x \rightarrow +\infty}{e^x \left (e - \left(1+\dfrac{1}{x}\right )^x\right)} = +\infty.$$ Is it possible find this limit without L'Hospital?
How to evaluate $\lim\limits_{x \rightarrow +\infty}{e^x (e - (1+\frac{1}{x} )^x)}$ without L'Hospital?
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calculus
limits
limits-without-lhopital
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1It is always possible to find a limit without l'Hopital as at some point l'Hopital was proving (hopefully without invoking l'Hopital). – 2012-08-15
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5what we allowed to use? – 2012-08-15
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0You are right. I never watched that. Thanks. – 2012-08-16