The answer is 3.
Given lim x->1 (x^3 - 1)/(x-1)
First, we need to convert numerator and denominator into simpler terms.
=> (x^3 - 1) / (x - 1)
=> (x^3 - 1^3) / (x - 1)
(x^3 - 1^3) can be written as (x - 1)(x^2 + x + 1^2) if we apply the formula
(a^3 - b^3) = (a-b)(a^2 + ab b^2)
=> (x - 1)(x^2 + x + 1^2) / (x-1)
=> x^2 + x + 1
Now, we re-write the given limit as lim x->1 (x^2 + x + 1). Substitute x = 1 in the expression, we get
1^2 + 1 + 1
= 1 + 1 + 1
= 3