lim→（-2）[x^2+x-2]/(根号6+x)-2求极限

Question

lim→（-2）[x^2+x-2]/(根号6+x)-2 求极限

Answer 1

lim(x→- 2) (x² + x - 2)/[√(6 + x) - 2]
= lim(x→- 2) [(x - 1)(x + 2)]/[√(6 + x) - 2] · [√(6 + x) + 2]/[√(6 + x) + 2]、分母有理化
= lim(x→- 2) {(x - 1)(x + 2)[√(6 + x) + 2]}/[(6 + x) - 4]
= lim(x→- 2) {(x - 1)(x + 2)[√(6 + x) + 2]}/(x + 2)
= lim(x→- 2) (x - 1)[√(6 + x) + 2]
= (- 2 - 1)[√(6 - 2) + 2]
= - 3 · 4
= - 12