Find-lim-x-x-2-ln-1-x-x-

Question Number 79679 by ~blr237~ last updated on 27/Jan/20

F i n d \lim_{x \to \infty} x^{2} l n (1 + x) - x

Commented by mathmax by abdo last updated on 27/Jan/20

l e t f (x) = x^{2} l n (1 + x) - x \Rightarrow f (x) = x^{2} l n (x (1 + \frac{1}{x})) - x

= x^{2} l n x + x^{2} l n (1 + \frac{1}{x}) - x \sim x^{2} l n x + x^{2} (\frac{1}{x}) - x \Rightarrow

f (x) \sim x^{2} l n x \Rightarrow {l i m}_{x \to + \infty} f (x) = + \infty

Commented by ~blr237~ last updated on 27/Jan/20

t h a n k s s i r