What is the

Question

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

Answer 1

the denominator factors as a difference of cubes

so lim (x-3)/(x^3 - 27) as x---> 3
= lim (x-3)/[(x-3)(x^2 + 3x + 9)] as x ---> 3
= lim 1/((x^2 + 3x + 9)
= 1/(9+9+9)
= 1/27