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GATE2007-28 [closed]

+1 vote

309 views

Consider the series $x_{n+1} = \frac{x_n}{2}+\frac{9}{8x_n},x_0 = 0.5$ obtained from the Newton-Raphson method. The series converges to

1.5
$\sqrt{2}$
1.6
1.4

closed with the note: Out of syllabus now

gate2007
numerical-methods
newton-raphson
normal
out-of-syllabus-now

asked Sep 22, 2014 in IS&Software Engineering by Kathleen Veteran (52.2k points)
closed Nov 6, 2016 by jothee | 309 views

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Answer:

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+4 votes

2 answers

1

GATE1996-2.5
Newton-Raphson iteration formula for finding $\sqrt[3]{c}$, where $c > 0$ is $x_{n+1}=\frac{2x_n^3 + \sqrt[3]{c}}{3x_n^2}$ $x_{n+1}=\frac{2x_n^3 - \sqrt[3]{c}}{3x_n^2}$ $x_{n+1}=\frac{2x_n^3 + c}{3x_n^2}$ $x_{n+1}=\frac{2x_n^3 - c}{3x_n^2}$

asked Oct 9, 2014 in Numerical Methods by Kathleen Veteran (52.2k points) | 444 views

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+5 votes

2 answers

2

GATE1999-1.23
The Newton-Raphson method is to be used to find the root of the equation $f(x)=0$ where $x_o$ is the initial approximation and $f’$ is the derivative of $f$. The method converges always only if $f$ is a polynomial only if $f(x_o) <0$ none of the above

asked Sep 23, 2014 in Numerical Methods by Kathleen Veteran (52.2k points) | 375 views

gate1999
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GATE2003-42
A piecewise linear function $f(x)$ is plotted using thick solid lines in the figure below (the plot is drawn to scale). If we use the Newton-Raphson method to find the roots of \(f(x)=0\) using \(x_0, x_1,\) and \(x_2\) respectively as initial guesses, the roots obtained ... 0.6 respectively 0.6, 0.6, and 1.3 respectively 1.3, 1.3, and 0.6 respectively 1.3, 0.6, and 1.3 respectively

asked Sep 17, 2014 in Numerical Methods by Kathleen Veteran (52.2k points) | 477 views

gate2003
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+1 vote

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GATE2008-22
The Newton-Raphson iteration $x_{n+1} = \frac{1}{2}\left(x_n+\frac{R}{x_n}\right)$ can be used to compute the square of R reciprocal of R square root of R logarithm of R

asked Sep 12, 2014 in Numerical Methods by Kathleen Veteran (52.2k points) | 502 views

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out-of-syllabus-now

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