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Which of the following statements applies to the bisection method used for finding roots of functions:

  1. converges within a few iterations

  2. guaranteed to work for all continuous functions

  3. is faster than the Newton-Raphson method

  4. requires that there be no error in determining the sign of the function

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The answer is B. 

The method is guaranteed to converge to a root of $f$ if $f$ is a continuous function on the interval $[a, b]$ and $f(a)$ and $f(b)$ have opposite signs. The absolute error is halved at each step so the method converges linearly, which is comparatively slow.

Refhttp://en.wikipedia.org/wiki/Bisection_method#Analysis

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