Reference no: EM13840368
Problem 1: Show graphically the e-x = sin(x/2) has at least one solution. Find an interval [a, b] containing the smallest solution, ?, for which the bisection method will converge to ?. Use the bisection method with a hand calculator or a computer to find the smallest root accurate to within ∈ = 0.01. Note: your answer should be justified and will depend on the choice of [a, b]. Produce a table of your iterates with the following columns: n, an, bn, cn, bn - cn. With a1 = a and b1 = b (Hand-written is fine.) for example:
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Problem 2: Let ? be the unique root of f(x). Find an interval [a, b] containing ? for which the bisection method will converge to ?. Then, estimate the number of iterates needed to find ? within an accuracy of ∈ = 10-9. Note: your answer should be justified and will depend on the choice of [a, b].
F(x) = x-3/1+x4
Problem 3: Show graphically that x = e-x has one solution. Use the bisection method with a hand calculator or computer to find the root accurate to within ∈ = 0.01. Produce a table of your iterates with the following columns: n, an, bn, cn, bn - cn. (Hand written is fine.) For example:
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Problem 4: Let ? be the unique root of f(x). Find an interval [a, b] containing ? for which the bisection method will converge to ?. Then, estimate the number of iterates needed to find ? within an accuracy or ∈ = 10-9. Note: Your answer should be justified and will depend on the choice of [a, b].
(a). f(x) = 31x3 - x2 + 27x - 2125
(b). f(x) = e2 - x - 2
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