Consider the function f(x) = 5x[sup]7[/sup] + 2x - 1 amd the associated equation f(x) = 0.
a) show (by hand) that there is a unique simple root r in the interval [0,1].
b) use bisection procedure (maple) to approximate r to eight corrent decimal places. Report the approximation xc, the number of steps needed and the backward error |f(xc)|
c) use the newton's method (maple) to approximate r to right corrent decimal places (starting with xo = 0). Report the approximation xc, number of steps needed and the backward error |f(xc)|.
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