Question

need help with 28,29,30

Write the formula for Newton's method and use the given initial approximation to compute the approximations X1 and x2. Round to six decimal places. 28) f(x) = e-x-ixo = In 4 Use a calculator to compute the first 10 iterations of Newton's method when applied to the function with the given initial approximation. Make a table for the values. Round to six decimal places. 29) f(x) = 3x - cos x; x0 = 1 Use Newton's method to approximate all the intersection points of the pair of curves. Some preliminary graphing or analysis may help in choosing good initial approximations. Round to six decimal places. 30) y=x3 - 2x2 and y=x2 - 3

Answer 1

according to the guidelines of HomeworkLib i have done first question please ask rest of the questions separately.....

(28) f(x) = ex-, = ln4 = 1.3862943611 f'(x)=- Ho = 1.38629 436 [Bt itration : +14) = f(1-38629 436) e-1-386294.5° 1.3 8629436= 0.01895094 f'(x) = re-1.38 9436 -0.16666667= -0.41666667 x = Hoof(xo) = 1.38629 436 – 0.01 895094 f'(xo) (-0.41666667) 1x, = 1.4317771 and itration : 1.431777 = 0.000254 f(x) = f(1.431777) = e. 6 54 790 -14 31777 -1.431777 f2)= (1.431777) --ė).4317 - = -0.405551 X = x,- f(x) O f(x₂) X2 = 1.431777- 0.000 25454790 (0.405551) - 1.432 405 * = 1.432405)