GATE EE 2017 Set 1 — Question 42
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Engineering Mathematics → Calculus
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Question
Only one of the real roots of lies in the interval and bisection method is used to find its value. For achieving an accuracy of 0.001, the required minimum number of iterations is _______.
Correct answer
10 to 10
Solution
In the bisection method, after iterations, the root is guaranteed to lie within an interval of length:To achieve an accuracy of , the length of the interval must be less than or equal to the desired accuracy:Given the interval , we have and . Substituting the values:We evaluate powers of 2:
Since , the minimum number of iterations required is .
Since , the minimum number of iterations required is .
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