Page 225 - Engineering Mathematics Workbook_Final

Numerical Methods

roots of the equation 1 x  2 and bisection method is
2 6x −
3
2
f ( ) x = − + 4x + 0.5x . The used to find its value. For achieving

correction x , to be added to X in an accuracy of 0.001, the required
ini
minimum number of iterations is
the first iteration is _______.
_____
[GATE-2015-CE-SET II]
[GATE-2017-EE-SESSION I]
87. The quadratic equation TRAPEZOIDAL RULE
x − 4x + = is the solved
2
4 0
nd
numerically starting with the initial 91. A 2 degree polynomial f(x) has
guess x = 3. The Newton-Raphson values of 1, 4 and 15 at x = 0, 1 and
respectively.
2,
The
0
integral
method is applied once to get a new  2
estimate and then the Secant method f ( ) x dx is to be estimated by
0
is applied once using the initial guess applying the Trapezoidal rule to this
and this new estimate. The estimated data. What is the error (defined as
value of the root after the application true value-approximate value) in the
of the Secant method is ______. estimate?
4
2
[GATE-2015-CE-SET I] (a) − (b) −
3 3
BISECTION METHOD
2
88. The bisection method is applied to (c) 0 (d) 3
compute a zero of the function
4
3
2
f ( ) x = x − x − x − 4 in the 92. Using the trapezoidal rule, and
dividing the interval of integration
interval [1, 9]. The method converges into three equal subintervals, the
to a solution after _____ interations. + 1
definite integral  x dx is _______
(a) 1 (b) 3 − 1

(c) 5 (d) 7 [GATE-2014-ME-SET 1]

[CS, GATE-2012, 2 MARKS] SIMPSON’S RULE

89. The real root of the equation 5x- 93. Simpson’s rule for integration gives
2cosx-1=0 (up to two decimal exact result when f(x) is a polynomial
accuracy) is ________ degree

[GATE-2014-ME-SET 2] (a) 1 (b) 2

90. Only one of the real roots of (c) 3 (d) 4
6
f ( ) x = x − − 1 lies in the interval [GATE-1993 (ME)]
x

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