Question

Lim x---> ∞

x-1
____
x+2

Answer 1

$\displaystyle \lim_{x\to\infty}\frac{x-1}{x+2}=\lim_{x\to\infty}\frac{x\left(1-\frac{1}{x}\right)}{x\left(1+\frac{2}{x}\right)}=\lim_{x\to\infty}\frac{1-\frac{1}{x}}{1+\frac{2}{x}}=\frac{1-\frac{1}{\infty}}{1+\frac{2}{\infty}}=\frac{1-0}{1+0}=1$