6. If the bisection algorithm is applied to a continuous function f(x) on an interval [a, b], where f(a) f(b) <0, then after n steps, an approximate root will have been computed with error of at most (A) (b-a)/2+1 (B)1/27/2 (C) (b-a)/22n (D)2n+1/(b-a).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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6. If the bisection algorithm is applied to a continuous function f(x) on an interval [a, b], where
f(a) f(b) < 0, then after n steps, an approximate root will have been computed with error of at most
-
(A) (b − a)/2n+1
(B)1/27/2
(C) (b − a)/2²n
-
(D)2n+¹/(b − a).
Transcribed Image Text:6. If the bisection algorithm is applied to a continuous function f(x) on an interval [a, b], where f(a) f(b) < 0, then after n steps, an approximate root will have been computed with error of at most - (A) (b − a)/2n+1 (B)1/27/2 (C) (b − a)/2²n - (D)2n+¹/(b − a).
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