解：lim [(x-2)/(x+1)]^xx→∞=lim [(x+1-3)/(x+1)]^xx→∞=lim {[1 +(-3)/(x+1)]^[-(x+1)/3]}⁻³·[1 +(-3)/(x+1)]⁻¹x→∞=e⁻³·(1+0)⁻¹=e⁻³·1=e⁻³
