Page 222 - Engineering Mathematics Workbook_Final

Numerical Methods

DIRECT METHOD 4x + 3
2
(d) X k+ 1 = k 2

70. In the interval 0, the equation x = 9x + 2
k
cos x has [GATE-2007-CE]

(a) No solution 73. Identify the Newton-Raphson

iteration scheme for finding the
(b) exactly one solution
square root of 2
(c) exactly two solution
1   2  
(d) an infinite number of solutions (a) x n+ 1 = 2    x + n x n   

[GATE-1995 (CS)]
1   2  
71. How many distinct values of x satisfy (b) x n+ 1 = 2   x − n x  
the equation sin(x) = x/2, where x is  n 
in radians? 2
(c) x n+ 1 =
(a) 1 (b) 2 x n

(c) 3 (d) 4 or more (d) x n+ 1 − 2 x
+
n
[GATE-2016]
[GATE-2007 (IN)]

NEWTON-RAPHSON METHOD
74. The recursion relation to solve
(TYPE-I) x e using Newton-Raphson
=
−
x
72. The following equation needs to be method is
numerically solved using the (a) x = e − n x
Newton-Raphson method n+ 1
x + 4x − = The Iterative (b) x = x − e − n x
3
9 0.
equation for this purpose is (k n+ 1 n
indicates the iteration level) e − n x
+
(c) x n+ 1 = (1 x n ) − n x
+
2x + 9 1 e
3
(a) X k+ = k
1
2
3X + 4 x − e − x n (1 x −
+
2
) 1
k
(d) x n+ 1 = n − n x n
2x + 4 x − e
2
n
(b) X = k
k+
1
3X + 9 [GATE-2008-EC]
2
k
2
(c) X k+ 1 = x − 3x + 4
k
k

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