Page 224 - Engineering Mathematics Workbook_Final

Numerical Methods

82. A piecewise linear function f(x) is   10 − 0.8     10 0  
plotted using thick solid lines in the (a)  0 − 0.6  (b)  0 10 
figure (the plot is drawn to scale).      
 0 − 0.8   10 0 
(c)     (d)    
  10 − 0.6    10 − 10 

[GATE-2011 EE]

f
84. The function ( ) x = e − x 1 is to be
solved using Newton-Raphson
method. If the initial value of x is
taken as 1.0, then the absolute error

nd
If we use the Newton-Raphson observed at 2 iteration is _____.
method to find the roots of f(x) = 0 [GATE-2014-EE-SET2]
using x , x and x respectively as
0
2
1
initial guesses, the roots obtained 85. In the Newton-Raphson method, an
would be initial guess of x = is made and
2
0
(a) 1.3, 0.6 and 0.6 respectively the sequence
, , ,......0.75x −
2
x x x 3 2x − 2x + =
4 0
(b) 0.6, 0.6 and 1.3 respectively 0 1 2
Consider the statements
(c) 1.3, 1.3 and 0.6 respectively
0
(i) x =
(d) 1.3, 0.6 and 1.3 respectively 3
[CS, GATE-2003, 2 MARKS] (ii) The method converges to a
solution in finite number of iterations
83. Solution of the variables x and x
2
1
for the following equations is to be Which of the following is TRUE?
obtained by employing the Newton-
Raphson iterative method (a) only (i)

=
x
Equation (i) 10 sin x − 1 0.8 0 (b) only (ii)
2
(c) Both (i) and (ii)
Equation (ii)
2
10x − 10 cos x − 0.6 0 (d) neither (i) nor (ii)
=
x
1
2
2
Assuming the initial values x = 0.0 [GATE-14 (CS-SET2)]
1
and x = 1.0, the Jacobian matrix is 86. In Newton Raphson iterative method,
2
the initial guess value ( x ) is
ini
considered as zero, while finding the

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