Question

help me olease!!!!!! im sooo confused

Answer 1

\[\lim_{x \rightarrow 1} ((\sqrt[3]{x}-1)/(\sqrt{x}-1)\]

Answer 2

how is it 0/0??

Answer 3

\[\text{ let } u=x^\frac{1}{6} => u^3=x^\frac{1}{2} \text{ and } u^2=x^\frac{1}{3}\]
so we have
\[\lim_{u \rightarrow 1}\frac{u^2-1}{u^3-1}=\lim_{x \rightarrow 1}\frac{(u-1)(u+1)}{(u-1)(u^2+u+1)}\]

Answer 4

\[\text{ since as } x-> 1 , u->1\]

Answer 5

\[\lim_{u \rightarrow 1}\frac{u+1}{u^2+u+1}=\frac{1+1}{1+1+1}=\frac{2}{3}\]