lim[(x^1/2-8)/(x^1/3-4)]x-->64

Question

lim[(x^1/2-8)/(x^1/3-4)]
x-->64

Answer 1

令t^6=x,则x^1/2=t³,x^1/3=t²
x-->64相当于t-->2
原式转为
lim(t³-8)/(t²-4)=lim(t-2)(t²+2t+4)/((t-2)(t+2))=lim(t²+2t+4)/(t+2)=(2²+2x2+4)/(2+2)=3
t→2 t→2 t→2