lim-x-3-x-2-x-x-2-

Question Number 28097 by tawa tawa last updated on 20/Jan/18

\lim_{x \to \infty} \frac{3^{x} - 2^{x}}{x^{2}}

Commented by abdo imad last updated on 20/Jan/18

= {l i m}_{x \to + \propto} \frac{3^{x} (1 - {(\frac{2}{3})}^{x})}{x^{2}} = {l i m}_{x \to + \propto} \frac{3^{x}}{x^{2}}

= {l i m}_{x \to + \propto} e^{x l n 3} e^{- 2 l n x} = {l i m}_{x \to + \propto} e^{x (l n 3 - 2 \frac{l n x}{x})}

= {l i m}_{x \to + \propto} e^{x l n 3} = + \propto b e c a u s e {l i m}_{x \to\propto} {(\frac{2}{3})}^{x} = 0

a n d {l i m}_{x \to + \propto} \frac{l n x}{x} = 0 .

Commented by çhëý böý last updated on 20/Jan/18

G o o d w o r k s i r

Commented by tawa tawa last updated on 21/Jan/18

God bless you sir