I used Newton-Raphson's method to find the approximate root of the equation 0 = 1+ x3 - 5x and it was 0.5 x, so the approximate root at the second step is (a) X2 = 0.221568 (b) x2 = 0.201568 %3D X2 = 0.241568 None of the above is correct (d)

Newton’s method for finding a root of f is to calculate x1, x2, ... via the iterative formula xk+1 = xk - f(xk) / f'(xk) starting from x0. For each of the following functions, calculate x1 and x2: (a) f(x) = 10 - x, with x0 =7 (b) f(x) = -x2 + 1, with x0 = 0

The number of bacteria in a container is given by an equation, Q(t)= Qoekt, where t is measured in hours. (a) Suppose that there are 8000 bacteria initially, and 13000 bacteria after 2 hours, find the value of k (correct to 5 decimal places). (b) Using the result in part (a), find the values of A, B, and C (correct to nearest integer). 0 t 1 2 3 4 Q(t) 8000 A B 16572 C

Find a root of f(x) = x²+1 -3 sin x with 10-3 accuracy. Please do not forget to mention the name of the method and the initial value(s) chosen.