Question

lim x→-8[ (√1-x)-3]/2+3次根号x 的极限是多少?

Answer 1

分子、分母同乘以 [√(1-x) +3]*[4 -2*x^(1/3) + x^(2/3)],则上式可以转化成：

=lim[√(1-x) -3][√(1-x) +3]*[4 -2*x^(1/3) + x^(2/3)]/{[√(1-x) +3]*[2+x^(1/3)]*[4 -2*x^(1/3) +x^(2/3)]}

=lim[(1-x) -9]*[4 -2*x^(1/3) +x^(2/3)]/{[√(1-x) +3]*[2^3 + x]}

=lim (-1)*(x+8)*[4 -2*x^(1/3) +x^(2/3)]/{[√(1-x) +3] * (x+8)}

=-1* lim[4 - 2*x^(1/3) +x^(2/3)]/[√(1-x) +3]

=-1* lim[4 - 2*(-8)^(1/3) + (-8)^(2/3)]/[√(1+8) + 3]

=-1* lim[4 - 2*(-2) + (-2)^2]/(3+3)

=-1* 12/6

=-2