lim-x-e-x-1-x-

Question Number 175994 by sciencestudent last updated on 10/Sep/22

l i \underset{x \to \infty}{m} \frac{e^{x} - 1}{x} = ?

Answered by JDamian last updated on 10/Sep/22

\infty

Answered by cortano2 last updated on 11/Sep/22

= \frac{e^{\infty} - 1}{\infty} = \frac{\infty}{\infty} = 1

Commented by Ar Brandon last updated on 11/Sep/22

e^{x} ≫ x as x \to + \infty

\lim_{x \to + \infty} \frac{e^{x} - 1}{x} \to + \infty

Answered by Raxreedoroid last updated on 11/Sep/22

\lim_{x \to \infty} \frac{e^{x} - 1}{x} (\frac{\infty}{\infty})

\lim_{x \to \infty} \frac{e^{x}}{1} = + \infty