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GATE20021.2
+1
vote
477
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The trapezoidal rule for integration gives exact result when the integrand is a polynomial of degree
0 but not 1
1 but not 0
0 or 1
2
gate2002
numericalmethods
trapezoidalrule
easy
asked
Sep 15, 2014
in
Numerical Methods
by
Kathleen
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1
Answer
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The degree of precision of trapezoidal rule is 1 so 1 or 0 is the correct answer but not more than that
answered
Sep 19, 2014
by
Bhagirathi
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GATE20022.15
The NewtonRaphson iteration $X_{n+1} = (\frac{X_n}{2}) + \frac{3}{(2X_n)}$ can be used to solve the equation $X^2 =3$ $X^3 =3$ $X^2 =2$ $X^3 =2$
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Sep 16, 2014
in
Numerical Methods
by
Kathleen
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173
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gate2002
numericalmethods
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+1
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1
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2
GATE2005IT2
If the trapezoidal method is used to evaluate the integral obtained $\int_{0}^{1} x^2dx$, then the value obtained is always > (1/3) is always < (1/3) is always = (1/3) may be greater or lesser than (1/3)
asked
Nov 3, 2014
in
Numerical Methods
by
Ishrat Jahan
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19.1k
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350
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gate2005it
numericalmethods
trapezoidalrule
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0
votes
1
answer
3
GATE2007IT22
The trapezoidal method is used to evaluate the numerical value of $\int_{0}^{1}e^x dx$. Consider the following values for the step size h. 102 103 104 105 For which of these values of the step size h, is the computed value guaranteed to be correct to ... Assume that there are no roundoff errors in the computation. iv only iii and iv only ii, iii and iv only i, ii, iii and iv
asked
Oct 30, 2014
in
Numerical Methods
by
Ishrat Jahan
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19.1k
points)

404
views
gate2007it
numericalmethods
trapezoidalrule
normal
outofsyllabusnow
0
votes
1
answer
4
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
asked
Sep 29, 2014
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Numerical Methods
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Kathleen
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258
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gate1997
numericalmethods
trapezoidalrule
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+5
votes
1
answer
5
GATE2014346
With respect to the numerical evaluation of the definite integral, $K = \int \limits_a^b \:x^2 \:dx$, where $a$ and $b$ are given, which of the following statements is/are TRUE? The value of $K$ obtained using the trapezoidal rule is always greater than or ... the Simpson's rule is always equal to the exact value of the definite integral. I only II only Both I and II Neither I nor II
asked
Sep 28, 2014
in
Numerical Methods
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jothee
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115k
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gate20143
numericalmethods
trapezoidalrule
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2
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6
GATE201323
Function $f$ is known at the following points: $x$ 0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3.0 $f(x)$ 0 0.09 0.36 0.81 1.44 2.25 3.24 4.41 5.76 7.29 9.00 The value of $\int_{0}^{3} f(x) \text{d}x$ computed using the trapezoidal rule is (A) 8.983 (B) 9.003 (C) 9.017 (D) 9.045
asked
Sep 24, 2014
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Numerical Methods
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Arjun
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396k
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751
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gate2013
numericalmethods
trapezoidalrule
nongate
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1
answer
7
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
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Sep 12, 2014
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Kathleen
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gate2008
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