Newton-Raphson-Method

Question 1
   
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
 
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
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.