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Recent questions and answers in Numerical Methods
+27
votes
3
answers
1
GATE20061, ISRO200957
Consider the polynomial $p(x) = a_0 + a_1x + a_2x^2 + a_3x^3$ , where $a_i \neq 0$, $\forall i$. The minimum number of multiplications needed to evaluate $p$ on an input $x$ is: 3 4 6 9
answered
Mar 17
in
Numerical Methods
by
immanujs
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3.2k
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gate2006
numericalmethods
normal
isro2009
+1
vote
1
answer
2
UGCNETJune2019II10
Consider an LPP given as $\text{Max } Z=2x_1x_2+2x_3$ subject to the constraints $2x_1+x_2 \leq 10 \\ x_1+2x_22x_3 \leq 20 \\ x_1 + 2x_3 \leq 5 \\ x_1, \: x_2 \: x_3 \geq 0 $ ... $x_1 = 0, x_2=0, \: x_3=10, \: Z=20$
answered
Oct 26, 2019
in
Numerical Methods
by
Roma_nagpal
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225
points)

254
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ugcnetjune2019ii
simplex
method
0
votes
1
answer
3
Is reading comprehension asked in IIITH
Does in iiith pgeee exam , does Reading comprehension is being asked. Do we need to prepare for it?
answered
Mar 29, 2019
in
Numerical Methods
by
Winner
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459
points)

98
views
iiithpgee
+4
votes
2
answers
4
ISRO200948
The cubic polynomial $y(x)$ which takes the following values: $y(0)=1, y(1)=0, y(2)=1$ and $y(3)=10$ is $x^3 +2x^2 +1$ $x^3 +3x^2 1$ $x^3 +1$ $x^3 2x^2 +1$
answered
Mar 10, 2019
in
Numerical Methods
by
Devwritt
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4.1k
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1k
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isro2009
polynomials
+1
vote
1
answer
5
UGC NET NOV 2017 PAPER 3 Q68
68. Consider the following LPP : Max Z=15x1+10x2 Subject to the constraints 4x1+6x2 ≤ 360 3x1+0x2 ≤ 180 0x1+5x2 ≤ 200 x1 , x2> / 0 The solution of the LPP using Graphical solution technique is : (1) x1=60, x2=0 and Z=900 (2) x1=60, x2=20 and Z=1100 (3) x1=60, x2=30 and Z=1200 (4) x1=50, x2=40 and Z=1150
answered
Mar 8, 2019
in
Numerical Methods
by
abhinav kumar
(
193
points)

683
views
0
votes
0
answers
6
UGCNETDEC2018II8
In PERT/CPM, the merge event represents _____ of two or more events. completion beginning splitting joining
asked
Jan 2, 2019
in
Numerical Methods
by
Arjun
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435k
points)

695
views
ugcnetdec2018ii
operationresearchpertcpm
0
votes
3
answers
7
GATE19943.4
Match the following items (i) NewtonRaphson (a) Integration (ii) RungeKutta (b) Root finding (iii) GaussSeidel (c) Ordinary Differential Equations (iv) Simpson's Rule (d) Solution of Systems of Linear Equations
answered
Dec 17, 2018
in
Numerical Methods
by
Gurdeep Saini
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gate1994
numericalmethods
easy
+8
votes
1
answer
8
ISRO200944
A root $\alpha$ of equation $f(x)=0$ can be computed to any degree of accuracy if a 'good' initial approximation $x_0$ is chosen for which $f(x_0) > 0$ $f (x_0) f''(x_0) > 0$ $f(x_0) f'' (x_0) < 0$ $f''(x_0) >0$
answered
Oct 7, 2018
in
Numerical Methods
by
Roman224
(
11
points)

1.9k
views
isro2009
numericalmethods
+1
vote
1
answer
9
UGC NET NOV 2017 PAPER Q69
69. Consider the following LPP : Min Z=2x1+x2+3x3 Subject to : x1−2x2+x3 / 4 2x1+x2+x3 £ 8 x1−x3 / 0 x1 , x2 , x3 / 0 The solution of this LPP using Dual Simplex Method is : (1) x1=0, x2=0, x3=3 and Z=9 (2) x1=0, x2=6, x3=0 and Z=6 (3) x1=4, x2=0, x3=0 and Z=8 (4) x1=2, xx2=0, x3=2 andZ=10
answered
May 11, 2018
in
Numerical Methods
by
Girjesh Chouhan
(
191
points)

1.4k
views
+1
vote
2
answers
10
Number Theory
A prison houses 100 inmates, one in each of 100 cells, guarded by a total of 100 warders. One evening, all the cells are locked and the keys left in the locks. As the first warder leaves, she turns every key, unlocking all the doors. The second warder ... every third key and so on. Finally the last warder turns the key in just the last cell. Which doors are left unlocked and why?
answered
Apr 19, 2018
in
Numerical Methods
by
Subarna Das
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17.8k
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166
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numbertheory
+6
votes
4
answers
11
ISRO20173
Using NewtonRaphson method, a root correct to 3 decimal places of $x^3  3x 5 = 0$ 2.222 2.275 2.279 None of the above
answered
Feb 27, 2018
in
Numerical Methods
by
stanchion
Junior
(
555
points)

5.2k
views
isro2017
newtonraphson
nongate
+1
vote
0
answers
12
UGCNETJune2014III60
The initial basic feasible solution of the following transportion problem: is given as 5 8 7 2 2 10 then the minimum cost is 76 78 80 82
asked
Nov 2, 2017
in
Numerical Methods
by
Naqvi
(
17
points)

273
views
ugcnetjune2014iii
transportationmethod
+1
vote
1
answer
13
GATE200821
The minimum number of equal length subintervals needed to approximate $\int_1^2 xe^x\,dx$ to an accuracy of at least $\frac{1}{3}\times10^{6}$ using the trapezoidal rule is 1000e 1000 100e 100
answered
Apr 25, 2017
in
Numerical Methods
by
Regina Phalange
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10k
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851
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gate2008
normal
numericalmethods
trapezoidalrule
nongate
+6
votes
2
answers
14
GATE2006IT28
The following definite integral evaluates to $\int_{\infty}^{0} e^ {\left(\frac{x^2}{20} \right )}dx$ $\frac{1}{2}$ $\pi \sqrt{10}$ $\sqrt{10}$ $\pi$
answered
Dec 30, 2016
in
Numerical Methods
by
Kai
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2.6k
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gate2006it
numericalmethods
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nongate
+1
vote
0
answers
15
GATE19881i
Loosely speaking, we can say that a numerical method is unstable if errors introduced into the computation grow at _________ rate as the computation proceeds.
asked
Dec 10, 2016
in
Numerical Methods
by
jothee
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106k
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128
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gate1988
nongate
numericalmethods
0
votes
0
answers
16
GATE198711b
Use Simpson's rule with $h=0.25$ to evaluate $ V= \int_{0}^{1} \frac{1}{1+x} dx$ correct to three decimal places.
[closed]
asked
Nov 15, 2016
in
Numerical Methods
by
makhdoom ghaya
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31.2k
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240
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gate1987
nongate
numericalmethods
simpsonsrule
0
votes
0
answers
17
GATE198711a
Given $f(300)=2,4771; f(304) = 2.4829; f(305) = 2.4843$ and $f(307) = 2.4871$ find $f(301)$ using Lagrange's interpolation formula.
[closed]
asked
Nov 15, 2016
in
Numerical Methods
by
makhdoom ghaya
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31.2k
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gate1987
nongate
numericalmethods
0
votes
0
answers
18
GATE19871xxv
Which of the following statements is true in respect of the convergence of the NewtonRephson procedure? It converges always under all circumstances. It does not converge to a tool where the second differential coefficient changes sign. It does not converge to a root where the second differential coefficient vanishes. None of the above.
[closed]
asked
Nov 9, 2016
in
Numerical Methods
by
makhdoom ghaya
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31.2k
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240
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gate1987
numericalmethods
nongate
newtonraphson
0
votes
0
answers
19
GATE19871xxiv
The simplex method is so named because It is simple. It is based on the theory of algebraic complexes. The simple pendulum works on this method. No one thought of a better name.
asked
Nov 9, 2016
in
Numerical Methods
by
makhdoom ghaya
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31.2k
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183
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gate1987
numericalmethods
simplexmethod
nongate
+3
votes
1
answer
20
UGCNETDec2014III69
Five men are available to do five different jobs. From past records, the time (in hours) that each man takes to do each job is known and is given in the following table : Find out the minimum time required to complete all the jobs. $5$ $11$ $13$ $15$
answered
Aug 2, 2016
in
Numerical Methods
by
Sanjay Sharma
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49.5k
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2.1k
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ugcnetdec2014iii
assignmentproblem
hungarianmethod
+3
votes
2
answers
21
ISRO201348
The GuassSeidal iterative method can be used to solve which of the following sets? Linear algebraic equations Linear and nonlinear algebraic equations Linear differential equations Linear and nonlinear differential equations
answered
Jun 29, 2016
in
Numerical Methods
by
kvkumar
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4.9k
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1.6k
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isro2013
numericalmethods
guassseidaliterativemethod
+3
votes
2
answers
22
ISRO200951
The formula $P_k = y_0 + k \triangledown y_0+ \frac{k(k+1)}{2} \triangledown ^2 y_0 + \dots + \frac{k \dots (k+n1)}{n!} \triangledown ^n y_0$ is Newton's backward formula Gauss forward formula Gauss backward formula Stirling's formula
answered
Jun 25, 2016
in
Numerical Methods
by
naga praveen
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3.9k
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isro2009
numericalmethods
+4
votes
1
answer
23
ISRO201152
Given X: 0 10 16 Y: 6 16 28 The interpolated value X=4 using piecewise linear interpolation is 11 4 22 10
answered
Jun 24, 2016
in
Numerical Methods
by
Kapil
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51k
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1.8k
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isro2011
interpolation
nongate
+3
votes
1
answer
24
ISRO200947
The formula $\int\limits_{x0}^{xa} y(n) dx \simeq h/2 (y_0 + 2y_1 + \dots +2y_{n1} + y_n)  h/12 (\triangledown y_n  \triangle y_0)$ $ h/24 (\triangledown ^2 y_n + \triangle ^2 y_0) 19h/720 (\triangledown ^3 y_n  \triangle ^3 y_0) \dots $ is called Simpson rule Trapezoidal rule Romberg's rule Gregory's formula
answered
Jun 15, 2016
in
Numerical Methods
by
ManojK
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38.7k
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isro2009
numericalmethods
nongate
+4
votes
1
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25
ISRO200946
The shift operator $E$ is defined as $E [f(x_i)] = f (x_i+h)$ and $E'[f(x_i)]=f (x_i h)$ then $\triangle$ (forward difference) in terms of $E$ is $E1$ $E$ $1E^{1}$ $1E$
answered
Jun 15, 2016
in
Numerical Methods
by
Kapil
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51k
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isro2009
+4
votes
2
answers
26
GATE20002.1
X, Y and Z are closed intervals of unit length on the real line. The overlap of X and Y is half a unit. The overlap of Y and Z is also half a unit. Let the overlap of X and Z be k units. Which of the following is true? k must be 1 k must be 0 k can take any value between 0 and 1 None of the above
answered
Jan 14, 2016
in
Numerical Methods
by
confused_luck
Junior
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903
points)

820
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gate2000
numericalmethods
normal
+5
votes
2
answers
27
GATE19991.23
The NewtonRaphson method is to be used to find the root of the equation $f(x)=0$ where $x_o$ is the initial approximation and $f’$ is the derivative of $f$. The method converges always only if $f$ is a polynomial only if $f(x_o) <0$ none of the above
answered
Jun 24, 2015
in
Numerical Methods
by
Rajarshi Sarkar
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33.9k
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407
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gate1999
numericalmethods
newtonraphson
normal
outofsyllabusnow
0
votes
1
answer
28
GATE19974.10
The trapezoidal method to numerically obtain $\int_a^b f(x) dx$ has an error E bounded by $\frac{ba}{12} h^2 \max f’’(x), x \in [a, b]$ where $h$ is the width of the trapezoids. The minimum number of trapezoids guaranteed to ensure $E \leq 10^{4}$ in computing $\ln 7$ using $f=\frac{1}{x}$ is 60 100 600 10000
answered
Jun 6, 2015
in
Numerical Methods
by
Digvijay Pandey
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gate1997
numericalmethods
trapezoidalrule
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+1
vote
2
answers
29
GATE19971.2
The NewtonRaphson method is used to find the root of the equation $X^22=0$. If the iterations are started from 1, the iterations will converge to 1 converge to $\sqrt{2}$ converge to $\sqrt{2}$ not converge
answered
Jun 5, 2015
in
Numerical Methods
by
Rajarshi Sarkar
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gate1997
numericalmethods
newtonraphson
normal
+4
votes
2
answers
30
GATE19962.5
NewtonRaphson iteration formula for finding $\sqrt[3]{c}$, where $c > 0$ is $x_{n+1}=\frac{2x_n^3 + \sqrt[3]{c}}{3x_n^2}$ $x_{n+1}=\frac{2x_n^3  \sqrt[3]{c}}{3x_n^2}$ $x_{n+1}=\frac{2x_n^3 + c}{3x_n^2}$ $x_{n+1}=\frac{2x_n^3  c}{3x_n^2}$
answered
Jun 4, 2015
in
Numerical Methods
by
Rajarshi Sarkar
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33.9k
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469
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gate1996
numericalmethods
newtonraphson
normal
outofsyllabusnow
0
votes
3
answers
31
GATE19952.15
The iteration formula to find the square root of a positive real number $b$ using the Newton Raphson method is $x_{k+1} = 3(x_k+b)/2x_k$ $x_{k+1} = (x_{k}^2+b)/2x_k$ $x_{k+1} = x_k2x_k/\left(x^2_k+b\right)$ None of the above
answered
Jun 2, 2015
in
Numerical Methods
by
Rajarshi Sarkar
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33.9k
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583
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gate1995
numericalmethods
newtonraphson
normal
0
votes
1
answer
32
GATE199301.3
In questions 1.1 to 1.7 below, one or more of the alternatives are correct. Write the code letter(s) a, b, c, d corresponding to the correct alternative(s) in the answer book. Marks will be given only if all the correct alternatives have been selected and no incorrect ... is picked up. 1.3 Simpson's rule for integration gives exact result when $f(x)$ is a polynomial of degree 1 2 3 4
answered
Apr 26, 2015
in
Numerical Methods
by
Rajarshi Sarkar
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33.9k
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715
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gate1993
numericalmethods
simpsonsrule
easy
+4
votes
1
answer
33
GATE2007IT77
Consider the sequence $\left \langle x_n \right \rangle,\; n \geq 0$ defined by the recurrence relation $x_{n + 1} = c \cdot (x_n)^2  2$, where $c > 0$. For which of the following values of $c$, does there exist a nonempty open interval $(a, b)$ such that the sequence $x_n$ ... $0.25$ $0.35$ $0.45$ $0.5$ i only i and ii only i, ii and iii only i, ii, iii and iv
answered
Apr 13, 2015
in
Numerical Methods
by
Rajarshi Sarkar
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33.9k
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597
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gate2007it
numericalmethods
normal
nongate
0
votes
2
answers
34
GATE2006IT27
Match the following iterative methods for solving algebraic equations and their orders of convergence. Method Order of Convergence 1. Bisection P. 2 or more 2. NewtonRaphson Q. 1.62 3. Secant R. 1 4. Regula falsi S. 1 bit per iteration IR, IIS, IIIP, IVQ IS, IIR, IIIQ, IVP IS, IIQ, IIIR, IVP IS, IIP, IIIQ, IVR
answered
Apr 12, 2015
in
Numerical Methods
by
Rajarshi Sarkar
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gate2006it
numericalmethods
normal
+2
votes
1
answer
35
GATE2004IT38
If f(l) = 2, f(2) = 4 and f(4) = 16, what is the value of f(3) using Lagrange's interpolation formula? 8 8(1/3) 8(2/3) 9
answered
Apr 7, 2015
in
Numerical Methods
by
Rajarshi Sarkar
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gate2004it
numericalmethods
lagrangesinterpolation
normal
+2
votes
2
answers
36
GATE2004IT39
Consider the following iterative root finding methods and convergence properties: Iterative root finding methods Convergence properties Q. False Position I. Order of convergence = 1.62 R. Newton Raphson II. Order of convergence = 2 S. Secant III. Order of convergence = 1 with guarantee of convergence T. Successive ... , RII, SI, TIV QII, RI, SIV, TIII QI, RIV, SII, TIII
answered
Apr 7, 2015
in
Numerical Methods
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Rajarshi Sarkar
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33.9k
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300
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gate2004it
numericalmethods
normal
+12
votes
3
answers
37
GATE2015350
The velocity $v$ (in kilometer/minute) of a motorbike which starts form rest, is given at fixed intervals of time $t$ (in minutes) as follows: t 2 4 6 8 10 12 14 16 18 20 v 10 18 25 29 32 20 11 5 2 0 The approximate distance (in kilometers) rounded to two places of decimals covered in 20 minutes using Simpson's $1/3^{rd}$ rule is ________.
answered
Feb 20, 2015
in
Numerical Methods
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ashishacm
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341
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1.7k
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gate20153
numericalmethods
simpsonsrule
normal
numericalanswers
+7
votes
2
answers
38
GATE2015239
The secant method is used to find the root of an equation $f(x)=0$. It is started from two distinct estimates $x_a$ and $x_b$ for the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if $f(x_b)$ is very small and then $x_b$ is the solution. ... $x_b  (x_bx_a) f_b / (f_bf(x_a)) $ $x_a  (x_bx_a) f_a / (f_bf(x_a)) $
answered
Feb 20, 2015
in
Numerical Methods
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Arjun
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gate20152
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0
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1
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39
calculus
The estimate of $\int_{0.5}^{1.5}\frac{dx}{x}$ obtained using Simpson’s rule with threepoint function evaluation exceeds the exact value by (A) 0.235 (B) 0.068 (C) 0.024 (D) 0.012
asked
Jan 30, 2015
in
Numerical Methods
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317
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numericalmethods
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nongate
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votes
0
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40
2012 numerical methed
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Jan 29, 2015
in
Numerical Methods
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115
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numericalmethods
outofsyllabusnow
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