Numerical Methods - Study Mode
[#46] Consider the series $${{ ext{x}}_{{ ext{n}} + 1}} = frac{{{{ ext{x}}_{ ext{n}}}}}{2} + frac{9}{{8{{ ext{x}}_{ ext{n}}}}},,{{ ext{x}}_0} = 0.5$$ xa0 xa0 xa0 obtained from the Newton-Raphson method. The series converges to
Correct Answer
(A) 1.5
[#47] The value of the function f(x) is given at n distinct values of x and its value is to be interpolated at the point x ⋆ , using all the n points. The estimate is obtained first by the Lagrange polynomial, denoted by $${I_{ ext{L}}}$$ and then by the Newton polynomial, denoted by $${I_{ ext{N}}}$$. Which one of the following statements is correct?
Correct Answer
(C) $${I_{ ext{L}}}$$ and $${I_{ ext{N}}}$$ are always equal
[#48] The extremum (minimum or maximum) point of a function f(x) is to be determined by solving $$frac{{{ ext{df}}left( { ext{x}}
ight)}}{{{ ext{dx}}}} = 0$$ xa0 using the Newton-Raphson method. Let f(x) = x 3 - 6x and x 0 = 1 be the initial guess of x. The value of x after two iterations (x 2 ) is
Correct Answer
(C) 1.4167
[#49] The accuracy of Simpson's rule quadrature for a step size h is
Correct Answer
(C) O(h 4 )
[#50] The table below gives values of a function F(x) obtained for values of x at intervals of 0.25. x 0 0.25 0.5 0.75 1.0 F(x) 1 0.9412 0.8 0.64 0.50 The value of the integral of the function between the limits 0 to 1 using Simpson's rule is
Correct Answer
(A) 0.7854