Page 216 - Engineering Mathematics Workbook_Final

Numerical Methods

nd
the solution at the end of the first is x = 1, then the value of x after 2
0
time step is __________ iteration is ____________.
[GATE-2017-CE SESSION-I] [GATE-2015-ME-SET-3]

31. There is no value of x that can 35. In Newton Raphson iterative method,
simultaneously satisfy both the given the initial guess value ( X ) is
ini
equation. Therefore, find the ‘least considered as zero, while finding the
squares error’ solution to the two roots of the equation
equations, i.e., find the value of x that ( ) x = − + 4x + 3
2 6x −
2
minimizes the sum of squares of the f 0.5x . The

errors in the two equations 2x = 3, 4x correction x , to be added to X in
ini
= 1. the first iteration is ______________.

32. Using given data points tabulated [GATE-2015-CE-SET-2]
below, a straight line passing through
the origin is fitted using least squares 36. The quadratic equation
2
4 0 is the solved
method. The slope of the line is x − 4x + =
numerically, starting with the initial
2
x y xy x guess x = 3. The Newton-Raphson
0
1 1.5 1.5 1 method is applied once to get a new
2 2.2 4.4 4 estimate and then the Secant method
3 2.7 8.1 9 is applied once using the initial guess
 xy = 14  x = 2 14 and this new estimate. The estimated

value of the root after the application
(a) 0.9 (b) 1 of the Secant method is __________.
(c) 1.1 (d) 1.5
[GATE-2015-CE-SET-1]

33. The Newton-Rapshon method is used 37. The Newton-Raphson method is used
to solve the equation to solve the equation
3
2
f ( ) x = x − 5x + 6x − = . Taking
8 0
3
2
f ( ) x = x − 5x + 6x − = .
8 0
the initial guess as x = 5, the solution
5
obtained at the end of the first Taking the initial guess as x = , the
iteration is ___________. solution obtained at the end of the
first iterations is _______.
[GATE-2015-ME-SET-2]
[GATE-2015-EC-SET-3]
34. Newton-Rapshon method is used to
find the roots of the equation, 38. How many distinct values of x satisfy
( )
x + 2x + 3x − 1 0. If the initial guess the equation sin x = x / 2, where x
=
2
3
is in radians?

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