Recent questions tagged newton-raphson - GATE Overflow

+6 votes

4 answers

1

ISRO2017-3
Using Newton-Raphson method, a root correct to 3 decimal places of $x^3 - 3x -5 = 0$ 2.222 2.275 2.279 None of the above

asked May 7, 2017 in Numerical Methods by sh!va Boss | 6.1k views

0 votes

0 answers

2

GATE1987-1-xxv
Which of the following statements is true in respect of the convergence of the Newton-Rephson procedure? It converges always under all circumstances. It does not converge to a tool where the second differential coefficient changes sign. It does not converge to a root where the second differential coefficient vanishes. None of the above.

asked Nov 9, 2016 in Numerical Methods by makhdoom ghaya Boss | 261 views

0 votes

1 answer

3

GATE2008-IT-30
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? 2.417 2.419 2.423 2.425

asked Oct 28, 2014 in IS&Software Engineering by Ishrat Jahan Boss | 294 views

+4 votes

2 answers

4

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 | 521 views

0 votes

3 answers

5

GATE1995-2.15
The iteration formula to find the square root of a positive real number $b$ using the Newton Raphson method is $x_{k+1} = 3(x_k+b)/2x_k$ $x_{k+1} = (x_{k}^2+b)/2x_k$ $x_{k+1} = x_k-2x_k/\left(x^2_k+b\right)$ None of the above

asked Oct 8, 2014 in Numerical Methods by Kathleen Veteran | 658 views

+1 vote

2 answers

6

GATE1997-1.2
The Newton-Raphson method is used to find the root of the equation $X^2-2=0$. If the iterations are started from -1, the iterations will converge to -1 converge to $\sqrt{2}$ converge to $\sqrt{-2}$ not converge

asked Sep 29, 2014 in Numerical Methods by Kathleen Veteran | 876 views

+6 votes

1 answer

7

GATE2014-2-46
In the Newton-Raphson method, an initial guess of $x_0= 2 $ is made and the sequence $x_0,x_1,x_2\:\dots$ is obtained for the function $0.75x^3-2x^2-2x+4=0$ Consider the statements $x_3\:=\:0$ The method converges to a solution in a finite number of iterations. Which of the following is TRUE? Only I Only II Both I and II Neither I nor II

asked Sep 28, 2014 in Numerical Methods by jothee Veteran | 641 views

+5 votes

2 answers

8

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 | 499 views

+1 vote

0 answers

9

GATE2007-28
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

asked Sep 22, 2014 in IS&Software Engineering by Kathleen Veteran | 342 views

+2 votes

1 answer

10

GATE2010-2
Newton-Raphson method is used to compute a root of the equation $x^2 - 13 = 0$ with 3.5 as the initial value. The approximation after one iteration is 3.575 3.676 3.667 3.607

asked Sep 21, 2014 in Numerical Methods by gatecse Boss | 967 views

0 votes

0 answers

11

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 | 513 views

+1 vote

1 answer

12

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 | 611 views

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