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What is limit `lim_(x -> 3)(x^3 - 27)/(x - 3)` . Do not use l'Hopital's rule

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xataexa | Student, Kindergarten | Salutatorian

Posted September 7, 2013 at 2:46 PM via web

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What is limit `lim_(x -> 3)(x^3 - 27)/(x - 3)` . Do not use l'Hopital's rule

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 7, 2013 at 2:50 PM (Answer #1)

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

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

Use the expansion `x^3 - 27 = (x - 3)(x^2 + 3x + 9)`

=` lim_(x -> 3)((x - 3)(x^2 + 3x + 9))/(x - 3)`

=` lim_(x -> 3)(x^2 + 3x + 9)`

substitute x = 3

= 9 + 9 + 9

= 27

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

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