Question

how to solve using change of variable:
lim
x->1 x^1/6 -1 / x^1/3 -1

Answer 1

Let \[u = x^1/6\]
then \[u^2 = x^1/3\]
change limit u(1) = 1
lim u --> 1 u-1/(u-1)(u+1)
\[\lim_{u \rightarrow 1} (1/u+1)=1/2\]