Question

Find the value of the limit:

Answer 1

\[\lim_{x \rightarrow \infty} x(1-\ln(1+\frac{ 1 }{ x })^x)\]

Answer 2

@mathmale @ganeshie8

Answer 3

I would use a substitution \(\displaystyle w=1+\frac{1}{x}\) and let \(w\to 1\)

Answer 4

the answer then follows easily by using L'Hospitals rule