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Question
Evaluate the following limit.
`lim_(z -> 1) (z^(1/3) - 1)/(z^(1/6) -1)`
Solution
We have, `lim_(z -> 1) (z^(1/3) - 1)/(z^(1/6) -1)` `(0/0 "form")`
= `lim_(z -> 1) ((z^(1/6))^2 - 1)/((z^(1/6) -1))`
= = `lim_(z -> 1) ((z^(1/6) - 1)(z^(1/6) + 1))/((z^(1/6) -1))`
= `lim_(z->1) (z^(1/6) + 1)`
= `1^(1/6) + 1`
= 1 + 1
= 2
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