Question

分子是根号3-根号(2+x),分母是1-开x的立方,x趋于1

Answer 1

lim[x→1][√3-(2+x)^(1/2)]/[1-x ^(1/3)]

=lim[x→1][-(1/2)(2+x)^(-1/2)]/[-(1/3)x ^(-2/3)] (0/0)

=lim[x→1][(3/2)[x ^(2/3)]/(2+x)^(1/2)]

=[(3/2)[1]/(2+1)^(1/2)

=(3/2)/3^(1/2)

=(3/2)/√3

=(1/2)√3