Consider the following non-linear equation: i. ii. iii. iv. 6e(-x)+ 5x² - 10x = 0 Let g(x) = e(-x)+²2 Show that x is the

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Consider The Following Non Linear Equation I Ii Iii Iv 6e X 5x 10x 0 Let G X E X 2 Show That X Is The 1 (91.69 KiB) Viewed 15 times

Consider the following non-linear equation: i. ii. iii. iv. 6e(-x)+ 5x² - 10x = 0 Let g(x) = e(-x)+²2 Show that x is the root of the given equation if and only if x is the midpoint of function g. Prove that the sucession X(n+1) = g(xn), n = 0,1, ... Converges to the only root of the function g at the interval I := xo E I. Calculate the iterations X1 and x2 obtained by the fixed point method given in ii, assuming xo = 1. Calculate the number of iterations that allow the absolute aproximation error less than 10 (-6). I it is not necessary to calculate the iterations. = [0,1], inspite of