can you answer my homework about math(limits!)?

Question

lim [(cuberoot of x) - (1)] / [x - 1]
x-->1

Answer 1

L'Hopital's Rule: if a fractional limit cannot be derived because it becomes 0 or infinity, then take the derivative of both parts.
lim x->1 of (x^(1/3) - 1) / (x-1)

Take the derivative:
f(x) = (x^(1/3) - 1)
f'(x) = 1/3x^(-2/3)
g(x) = x - 1
g'(x) = 1

So:
lim x-> 1 = 1/3x^(-2/3) / 1 = 1 / (3x^(2/3)) (solution!)