Question

Lim (x->inf) ((x-5)/(x+2))^(2x+10)

Answer 1

$\lim_{x \to \infty} (\frac{x-5}{x+2} )^{2x+10}= \lim_{x \to \infty} (1+\frac{-7}{x+2} )^{\frac{x+2}{-7}*\frac{-7}{x+2}*(2x+10)}=\\ = \lim_{x \to \infty} e^{\frac{-14(x+5)}{x+2}}= e^{ -14\lim_{x \to \infty} \frac{x+5}{x+2}} =e^{-14}$