What is the limit and how to do it. lim x->1 ((x^3)-1)/((x^4)-1)
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ugabulldog
ANSWERS: 1
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You have to factor numerator & denominator to reduce to lowest terms. x^3 - 1 = (x-1)(x^2 + x + 1) (basic algebra?) x^4 - 1 = (x^2 + 1)(x^2 - 1) (diff of 2 squares) = (x^2 + 1)(x + 1)(x - 1) (ditto) So there's a common factor of (x - 1) When you divide this out, you get the expression: (x^2 + x + 1) / [(x^2 + 1)(x + 1)] Now you can substitute the limit value (x=1) which gives a finite answer. The very last step is left to you!
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