Explain how you know what number is missing in the equation 3,947 = 3,000 + +40+7
2 answers:
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Answer:
n = 29 iterations would be enough to obtain a root of that is at most
away from the correct solution.
Step-by-step explanation:
You can use this formula which relates the number of iterations, n, required by the bisection method to converge to within an absolute error tolerance of ε starting from the initial interval (a, b).
We know
a = -2, b = 1 and ε = so
Thus, n = 29 iterations would be enough to obtain a root of that is at most
away from the correct solution.
<u>You can prove this result by doing the computation as follows:</u>
From the information given we know:
This is the algorithm for the Bisection method:
- Find two numbers <em>a</em> and <em>b</em> at which <em>f</em> has different signs.
- Define
- If
then accept c as the root and stop
- If
then set <em>c </em>as the new<em> b</em>. Otherwise, set <em>c </em>as the new <em>a</em>. Return to step 1.
We know that and
so we take
and
then
Because we set
as the new <em>b.</em>
The bisection algorithm is detailed in the following table.
After the 29 steps we have that hence the required root approximation is c = -0.50
