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GATE IT 2008 | Question: 30

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Consider the function f(x) = x2 - 2x - 1. Suppose an execution of the Newton-Raphson method to find a zero of f(x) starts with an approximation x0 = 2 of x. What is the value of x2, the approximation of x that algorithm produces after two iterations, rounded to three decimal places?

  1. 2.417
  2. 2.419
  3. 2.423
  4. 2.425
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In newton method, if current guess is xcur, then new guess xnew is

xnew = xcur - f(xcur)/f'(xcur)

Now Initially, xcur = 2, so after 1st iteration,

xnew = 2 - (-1)/2 = 2.5

Now xcur becomes 2.5, so after 2nd iteration,

xnew = 2.5 - (0.25)/3 = 2.417

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