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