Page 217 - Engineering Mathematics Workbook_Final

Numerical Methods

(a) 1 (b) 2 an accuracy of 0.001, the required
minimum number of iterations is
(c) 3 (d) 4 or more
___________.

[GATE-2016; 1 MARK]
[GATE 2017 – EE – SESSION-1]
39. The root of the function 0.2
3
f ( ) x = x + − 1 obtained after first 43. What is the value of (1525 ) to 2
x
decimal places?
iteration on application of Newton
Raphson scheme using an initial (a) 4.33 (b) 4.36
guess of x = 1 is
0
(c) 4.38 (d) 4.30
(a) 0.682 (b) 0.686
[ESE 2018 (Common Paper)]

(c) 0.750 (d) 1.000 44. The quadratic equation

2
3 0
[GATE 2016 – ME – SET-1] 2x − 3x + = to be solved
numerically starting with an initial
40. Newton-Raphson method is to be
2
used to find root of equation guess as x = . The new estimate of
0
−
3x e + sin x = . If the initial trial x after the first iteration using
x
0
value for the root is taken as 0.333, Newton-Raphson method is _______.
the next approximation for the root
would be _________ (note: answer [GATE 2018 (CE – Afternoon Session)]
upto there decimal)
45. What is the cube root of 1468 to 3
[GATE 2016 – CE – SET-1] decimal places?

41. To solve the equation 2 sin x = x by (a) 11.340 (b) 11.353

Newton-Raphson method, the initial (c) 11.365 (d) 11.382
guess was chosen to be x = 2.0.
Consider x in radian only. The value [ESE 2018 (Common Paper)]
of x (in radian) obtained after one th
iteration will be closest to 46. The following table lists an n order
polynomial

(a) -8.101 (b) 1.901 f ( ) x = a x + a x n− 1 + ......... a x a 0
+
n
+
n−
1
n
1
(c) 2.099 (d) 12.101 and the forward differences
evaluated at equally spaced values of
[GATE 2016 (PI)] x. The order of the polynomial is
42. Only one of the real roots of
6
x
f ( ) x = x − − 1lies in the interval
1 x  2 and bisection method is

used to find its value. For achieving

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