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What is limit x -> 3 (x^3 - 27)/(x - 3) 

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carolinesmiths | Student, Kindergarten | (Level 1) Salutatorian

Posted September 7, 2013 at 2:34 PM via web

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What is limit x -> 3 (x^3 - 27)/(x - 3) 

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 7, 2013 at 2:38 PM (Answer #1)

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The limit `lim_(x->3) (x^3 - 27)/(x - 3)` has to be determined.

Substituting x = 3 gives the indeterminate form `0/0` . Use l'Hopital's rule and replace the numerator and denominator with their derivatives.

This gives:

`lim_(x->3) (x^3 - 27)/(x - 3)`

= `lim_(x->3) (3x^2)/(1)`

= 3*9

= 27

The limit `lim_(x->3) (x^3 - 27)/(x - 3) = 27`

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