lim-x-x-a-x-a-x-

Question Number 111442 by bobhans last updated on 03/Sep/20

\lim_{x \to \infty} {(\frac{x + a}{x - a})}^{x} ?

Answered by bemath last updated on 03/Sep/20

Answered by ajfour last updated on 03/Sep/20

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

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

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

\ln L = 2 a

L = e^{2 a} .

Answered by Dwaipayan Shikari last updated on 03/Sep/20

\lim_{x \to \infty} {(1 + \frac{2 a}{x - a})}^{\frac{x}{2 a} . \frac{x - a}{x - a} . 2 a}

= e^{\frac{2 a x}{x - a}} = e^{2 a}