evaluate-Lim-x-xln-x-1-x-

Question Number 73552 by Rio Michael last updated on 13/Nov/19

e v a l u a t e

\underset{x \to + \infty}{L i m} x l n (\frac{x + 1}{x})

Commented by mathmax by abdo last updated on 13/Nov/19

w e h a v e x l n (\frac{x + 1}{x}) = x l n (1 + \frac{1}{x}) = x (\frac{1}{x} + o (\frac{1}{x^{2}})) = 1 + o (\frac{1}{x}) (x \to + \infty)

\Rightarrow {l i m}_{x \to + \infty} x l n (\frac{x + 1}{x}) = 1

Answered by ajfour last updated on 13/Nov/19

L = \lim_{x \to \infty} \frac{\ln (1 + \frac{1}{x})}{(\frac{1}{x})} = 1

Commented by Rio Michael last updated on 13/Nov/19

t h a n k s