Question

How do you find the limit of `(x^(2/3) -(2sqrt x)) /( 4 - (16/x))` as x approaches 8?

Answer 1

We have that

#lim_(x->8) (x^(2/3) -(2sqrt x)) /( 4 - (16/x))= [8^(2/3)-2sqrt8]/[4-16/8]=[4-4sqrt2]/[2]= 2-2sqrt2#