Since the derivative of sin(x) is cos(x) and the derivative of 96x is 96, applying L'Hospital's Rule a fourth time gives us the following. sin(x) = lim cos(x) lim x-0 96x 018 96 Therefore, we have the following result. cos(x) - 1 + lim X10 +1x2 = lim 4x4 x-0 X - sin(x) 16x3 = lim X-O 1 - cos(x) 48x2 sin(x) = lim == lim x-0 96x 0-x cos(x) 96 =