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

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justaguide eNotes educator| Certified Educator

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`