Newton-Raphson-Method

 Question 1
In the Newton-Raphson method, an initial guess of x0 = 2 is made and the sequence x0, x1, x2 … is obtained for the function
```0.75x3 – 2x2 – 2x + 4 = 0

Consider the statements
(I) x3 = 0.
(II) The method converges to a solution in a finite number of iterations.```
Which of the following is TRUE?
 A Only I B Only II C Both I and II D Neither I nor II
Engineering-Mathematics       Newton-Raphson-Method       Gate 2014 Set -02
Question 1 Explanation:
Note: Numerical methods are not in GATE CS syllabus.
 Question 2
Newton-Raphson method is used to compute a root of the equation x2 - 13 = 0 with 3.5 as the initial value. The approximation after one iteration is
 A 3.575 B 3.676 C 3.667 D 3.607
Engineering-Mathematics       Newton-Raphson-Method       2010
Question 2 Explanation:
Note: Out of syllabus.
 Question 3
The Newton-Raphson iteration can be used to compute the
 A square of R B reciprocal of R C square root of R D logarithm of R
Engineering-Mathematics       Newton-Raphson-Method       Gate-2008
Question 3 Explanation:
Note: Out of syllabus.
 Question 4
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 0f x. What is the value of x2, 'the approximation of x' that the algorithm produces after two iterations, rounded to three decimal places?
 A 2.417 B 2.419 C 2.423 D 2.425
Engineering-Mathematics       Newton-Raphson-Method       Gate 2008-IT
Question 4 Explanation:
Note: Out of syllabus.
 Question 5

 A 1.5 B √2 C 1.6 D 1.4
Engineering-Mathematics       Newton-Raphson-Method       Gate-2007
Question 5 Explanation:
Given series is xn+1=xn/2+9/8xn ⟶ (I); x0=0.5
Equation based on Newton-Rapson is
xn+1=xn-f(xn)/f'(xn)⟶ (II)
Equate I and II
xn-f(xn)/f'(xn)=xn/2+9/8xn
xn-f(xn)/f'(xn)=xn-xn/2+9/8xn
xn-f(xn)/f'(xn)=xn-(4xn2-9)/8xn
So, f(x)=4xn2-9
4x2-9=0
4x2=9
x2=9/4
x=±3/2
x=±1.5
 Question 6
A piecewise linear function f(x) is plotted using thick solid lines in the figure below If we use the Newton-Raphson method to find the roots of f(x) = 0 using x0, x1 and x2 respectively as initial guesses, the roots obtained would be
 A 1.3, 0.6, and 0.6 respectively B 0.6, 0.6, and 1.3 respectively C 1.3, 1.3, and 0.6 respectively D 1.3, 0.6, and 1.3 respectively
Engineering-Mathematics       Newton-Raphson-Method       Gate-2003
Question 6 Explanation:
Note: Out of syllabus.
 Question 7

 A X2 = 3 B X3 = 3 C X2 = 2 D X3 = 2
Engineering-Mathematics       Newton-Raphson-Method       Gate-2002
Question 7 Explanation:
Newton Rampson formula,
 Question 8
The Newton-Raphson method is to be used to find the root of the equation f(x)=0 where xo is the initial approximation and f' is the derivative of f. The  method converges
 A always B only if f is a polynomial C only if f(x0) < 0 D None of the above
Engineering-Mathematics       Newton-Raphson-Method       Gate-1999
Question 8 Explanation:
Note: Out of syllabus.
 Question 9
The Newton-Raphson method is used to find the root of the equation x2 − 2 = 0. If the iterations are started form –1, the iterations will
 A converge to -1 B converge to √2 C converge to - √2 D not converge
Engineering-Mathematics       Newton-Raphson-Method       Gate-1997
Question 9 Explanation:
 Question 10

 A B C D
Engineering-Mathematics       Newton-Raphson-Method       Gate-1996
Question 10 Explanation:
Note: Out of syllabus.
 Question 11
The iteration formula to find the square root of a positive real number b using the Newton Raphson method is
 A B C D None of the above
Engineering-Mathematics       Newton-Raphson-Method       Gate-1995
Question 11 Explanation:
Note: Out of syllabus.
There are 11 questions to complete.