Evaluate the Limit

Question

The limit

lim x approaches infinity sqrt ( x^2+3x+12 ) - x

Answer 1

lim x→∞ [√(x² + 3x + 12) - x] = lim x→∞ (3x + 12)/[√(x² + 3x + 12) + x] = lim x→∞ (3 + 12/x)/[√1 + 3/x + 12/x²) + 1] = (3 + 0)/[√(1 + 0 + 0) + 1] = 3/2