limit(2)

lim(x→∞) √[x³ / (x-1)] - x= lim(x→∞) (√[x³ / (x-1)] - x) (√[x³ / (x-1)] + x) / (√[x³ / (x-1)] + x)= lim(x→∞) (x³ / (x-1) - x²) / (√[x³ / (x-1)] + x)= lim(x→∞) [x² / (x-1)] / (√[x³ / (x-1)] + x)= lim(x→∞) x² / [√[x³ (x-1)] + x(x-1)]= lim(x→∞) x / [√[x(x-1)] + (x-1)]= lim(x→∞) 1 / [√(1 - 1/x) + 1 - 1/x]= 1 / [√(1 - 0) + 1 - 0]= 1/2

the correct answer is 1/2

http://www.wolframalpha.com/input/?i=sqrt%28x^3%2F%28x-1%29%29-x