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Question
Evaluate the following limits: `lim_(u -> 1)[(u^4 - 1)/(u^3 - 1)]`
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Solution
`lim_(u -> 1)[(u^4 - 1)/(u^3 - 1)]`
= `lim_(u -> 1)([(u^4 - 1^4)/(u - 1)])/([(u^3 - 1^3)/(u - 1)]) ...[(because u ->1";" u ≠ 1),(therefore u - 1 ≠ 0)]`
= `(4(1)^2)/(3(1)^2) ...[because lim_(x -> "a") (x^"n" - "a"^"n")/(z - "a") = "na"^("n" - 1)]`
= `4/3`
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