Question

Evaluate the limit of (x^1/6 -1) / (x^1/3 -1) as x approaches 1 by using a change of variable

Answer 1

no change needed, since x^1/3 - 1 = (x^1/6 - 1)(x^1/6 + 1)
so the quotient is 1/(x^1/6 + 1) for everywhere except x=1.
So the limit is 1/2