limx→27((x-27)/(x^(1/3)-3))

问题描述:

limx→27((x-27)/(x^(1/3)-3))

因为x-27=(x^(1/3)-3))[x^(2/3)+3x^(1/3)+9]
所以((x-27)/(x^(1/3)-3))=x^(2/3)+3x^(1/3)+9
所以,原极限=limx→27[x^(2/3)+3x^(1/3)+9]=9+9+9=27