How would I find the limit of (if it exists):

Question

lim x-->3 (x^3-27)
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(x^2-9)

Answer 1

It might look better this way...

lim x-->3 (x^3 -27)/(x^2 -9)

Answer 2

it factors

lim x-->3 (x^3 -27)/(x^2 -9) ax x--->3
= lim [(x-3)(x^2 + 3x + 9)]/[(x+3)(x-3)]
= lim (x^2 + 3x + 9)/(x+3)
= (9+9+9)/(3+3)
= 9/2