[math]\lim_{x\to\infty}{x \left[e-\left(1+\frac{1}{x}\right)^x\right]}[/math]I tried to use [imath]e^{\ln f(x)}[/imath] and L'Hospital rule but both didn't work.
I think this limit is similar to [math]\lim_{x\to0}{\frac{e-(1+x)^\frac{1}{x}}{x}}[/math][math][/math] but not, it's hard much more this one.
I'm very grateful if you could help me
I think this limit is similar to [math]\lim_{x\to0}{\frac{e-(1+x)^\frac{1}{x}}{x}}[/math][math][/math] but not, it's hard much more this one.
I'm very grateful if you could help me