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13 Nov 2019
8. Let /(x)=-x+1. a. Use Newton's method with1.5 to approximate a solution places of accuracy. e. Graph fusing a window of [-3,2ê²-2.5] and explain gemmetrically why Ne s step illustrates the importance of choosing a good initial a b. Why does Newton's method fail if x0 =-17 of x5 / 5-x + 1-0 with 6 decimal 9. This Newon's method fails if chosen value of xo can lead to unexpected results. The graph of f(x)-sinx (Figure 5) indicates that there are three roots off(x) = 0: They are x = 0 and two roots near x value of x0 049. Calculate the approximations x,,x2, x3 b, what happens if you use a starting value of xo = 0.4 instead? c. What happens if you use a starting value of 0.6 instead? a. Suppose we wish to verify that Newton's method approximates the known root x-O by using an initial decimal places. What happens and why? ation x to the root r. A poorly 1 and x =-1. until two consecutive values agree to 6 0,5 -0.5 0.5 1 -0.5 Figure 5
8. Let /(x)=-x+1. a. Use Newton's method with1.5 to approximate a solution places of accuracy. e. Graph fusing a window of [-3,2ê²-2.5] and explain gemmetrically why Ne s step illustrates the importance of choosing a good initial a b. Why does Newton's method fail if x0 =-17 of x5 / 5-x + 1-0 with 6 decimal 9. This Newon's method fails if chosen value of xo can lead to unexpected results. The graph of f(x)-sinx (Figure 5) indicates that there are three roots off(x) = 0: They are x = 0 and two roots near x value of x0 049. Calculate the approximations x,,x2, x3 b, what happens if you use a starting value of xo = 0.4 instead? c. What happens if you use a starting value of 0.6 instead? a. Suppose we wish to verify that Newton's method approximates the known root x-O by using an initial decimal places. What happens and why? ation x to the root r. A poorly 1 and x =-1. until two consecutive values agree to 6 0,5 -0.5 0.5 1 -0.5 Figure 5