lim-x-x-x-3-x-1-

Question Number 126599 by liberty last updated on 22/Dec/20

\lim_{x \to \infty} (x + \sqrt{\frac{x^{3}}{x - 1}})

Answered by bramlexs22 last updated on 22/Dec/20

\lim_{x \to \infty} (x + x \sqrt{\frac{x}{x - 1}}) =

\lim_{x \to \infty} x (1 + \sqrt{\frac{1}{(\frac{x - 1}{x})}}) =

\lim_{x \to \infty} x (1 + \sqrt{\frac{1}{1 - \frac{1}{x}}})

l e t \frac{1}{x} = p \land p \to 0

\lim_{p \to 0} \frac{1 + \sqrt{\frac{1}{1 - p}}}{p} = \infty