lim x-->3 x^2 -9 / x^3 - 27
please show steps
the answer is suppose to be 2/9
please show steps
the answer is suppose to be 2/9
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Recall the following identities:
x^2 -9 = (x-3)(x+3)
x^3 - 27 = (x-3)(x^2 + 3x + 9)
So, for x =/= 3 :(x^2 -9)/( x^3 - 27) = (x+3)/(x^2 + 3x + 9)
Therefore, the limit as x-->3 is 6/(9+9+9) = 2/9
x^2 -9 = (x-3)(x+3)
x^3 - 27 = (x-3)(x^2 + 3x + 9)
So, for x =/= 3 :(x^2 -9)/( x^3 - 27) = (x+3)/(x^2 + 3x + 9)
Therefore, the limit as x-->3 is 6/(9+9+9) = 2/9