4.8 Homework - Newton's Method (Homework)

6. [-/1 Points] DETAILS SCALCET9 4.8.021. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use Newton's method to find all solutions of the equation correct to six decimal places. (Enter your answers as a comma-separated list.) arctan(x) = x2 - 4 Need Help? Read It 7. [-/1 Points] DETAILS SCALCET9 4.8.027. MY NOTES ASK YOUR TEACHER A graphing calculator is recommended. Use Newton's method to find all solutions of the equation correct to eight decimal places. Start by looking at a graph to find initial approximations. (Enter your answers as a comma-separated list.) V5- x3 =6 X = Need Help? Read It8. [-/1 Points] DETAILS SCALCET9 4.8.032. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER (a) Use Newton's method with x, = 1 to find the root of the equation x - x = 5 correct to six decimal places. X = (b) Solve the equation in part (a) using x1 = 0.6 as the initial approximation. X = (c) Solve the equation in part (a) using x, = 0.57. (You definitely need a programmable calculator for this part.) X = (d) Graph f(x) = x5 - x - 5 and its tangent lines at x, = 1, 0.6, and 0.57. y 6/ X1 = 0.6 X1 = 0.57 -1.0 -0.5 0.5 1.0 1.5 2.0 -1.0 -0.5 0.5 1.0 1.5 2.0 -1 -21 -21 - X -3- -1.0 P.5 0.5 1.0 - 3 4- -4 = 1 X1 =1 1 X1 = 0.6- X1 = 0.57 -1.0 -0.5 ).5 1.0 1.5 X1 = 0.57 X1 = 0.6 X1 = 0.57 x1 = 0.6/ O -61 Need Help? Read It9. [-/1 Points] DETAILS SCALCET9 4.8.036.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use Newton's method to find the absolute maximum value of the function f(x) = 2x cos(x), OSXSI, correct to six decimal places. Need Help? Read It Master It 10. [-/1 Points] DETAILS SCALCET9 4.8.038. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Of the infinitely many lines that are tangent to the curve y = -6 sin(x) and pass through the origin, there is one that has the largest slope. Use Newton's method to find the slope of that line correct to six decimal places. Need Help? Read It