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3 answers
1
GATE CSE 2008 | Question: 21
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
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...
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4 votes
2 answers
3
ISRO2009-48
The cubic polynomial $y(x)$ which takes the following values: $y(0)=1, y(1)=0, y(2)=1$ and $y(3)=10$ is $x^3 +2x^2 +1$ $x^3 +3x^2 -1$ $x^3 +1$ $x^3 -2x^2 +1$
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$$x^3 -2x^2 +1$
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3 votes
2 answers
5
GATE CSE 1997 | Question: 1.2
The Newton-Raphson method is used to find the root of the equation $X^2-2=0$. If the iterations are started from -1, the iterations will converge to -1 converge to $\sqrt{2}$ converge to $\sqrt{-2}$ not converge
The Newton-Raphson method is used to find the root of the equation $X^2-2=0$. If the iterations are started from -1, the iterations willconverge to -1converge to $\sqrt{2...
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3 votes
1 answer
8
GATE IT 2004 | Question: 38
If f(l) = 2, f(2) = 4 and f(4) = 16, what is the value of f(3) using Lagrange's interpolation formula? 8 8(1/3) 8(2/3) 9
If f(l) = 2, f(2) = 4 and f(4) = 16, what is the value of f(3) using Lagrange's interpolation formula?88(1/3)8(2/3)9
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10
NIELIT 2021 Dec Scientist B - Section B: 60
One root of $x^{3} – x – 4 = 0$ lies in $(1, 2).$ In bisection method, after first iteration the root lies in the interval ___________ . $(1, 1.5)$ $(1.5, 2)$ $(1.25, 1.75)$ $(1.75, 2)$
One root of $x^{3} – x – 4 = 0$ lies in $(1, 2).$ In bisection method, after first iteration the root lies in the interval ___________ .$(1, 1.5)$$(1.5, 2)$$(1.25, 1....
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11
Numerical Method Analysis : Help...
Use Bisection method to find the root of the following equation with tolerance 0.001. $x^4 - 2x^3 - 4x^2 + 4x + 4 = 0$ $x^3 – e^x + sin(x) = 0$
Use Bisection method to find the root of the following equation with tolerance 0.001.$x^4 - 2x^3 - 4x^2 + 4x + 4 = 0$$x^3 – e^x + sin(x) = 0$
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12
Numerical Method Analysis : Help...
Use Bisection method to find all roots of $x^3 – 5x + 3 = 0$
Use Bisection method to find all roots of $x^3 – 5x + 3 = 0$
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13
Numerical Method Analysis : Help....
Use NR method to find a root of the equation with tolerance x=0.00001. $x^3-2x-5=0$ $e^x-3x^2=0$
Use NR method to find a root of the equation with tolerance x=0.00001.$x^3-2x-5=0$$e^x-3x^2=0$
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14
Numerical Method Analysis : Help...
Use Secant method to find roots of: $x^3-2x^2+3x-5=0$ $x+1 = 4sinx$ $e^x = x + 2$
Use Secant method to find roots of:$x^3-2x^2+3x-5=0$$x+1 = 4sinx$$e^x = x + 2$
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1 votes
1 answer
15
GATE CSE 1987 | Question: 1-xxiv
The simplex method is so named because It is simple. It is based on the theory of algebraic complexes. The simple pendulum works on this method. No one thought of a better name.
The simplex method is so named because It is simple.It is based on the theory of algebraic complexes.The simple pendulum works on this method.No one thought of a better n...
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1 answer
16
NIELIT 2016 MAR Scientist B - Section B: 7
In which of the following methods proper choice of initial value is very important? Bisection method False position Newton-Raphson Bairsto method
In which of the following methods proper choice of initial value is very important?Bisection methodFalse positionNewton-RaphsonBairsto method
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8 votes
3 answers
18
GATE IT 2006 | Question: 28
The following definite integral evaluates to $\int_{-\infty}^{0} e^ {-\left(\frac{x^2}{20} \right )}dx$ $\frac{1}{2}$ $\pi \sqrt{10}$ $\sqrt{10}$ $\pi$
The following definite integral evaluates to$$\int_{-\infty}^{0} e^ {-\left(\frac{x^2}{20} \right )}dx$$$\frac{1}{2}$$\pi \sqrt{10}$$\sqrt{10}$$\pi$
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3 answers
20
GATE CSE 1995 | Question: 2.15
The iteration formula to find the square root of a positive real number $b$ using the Newton Raphson method is $x_{k+1} = 3(x_k+b)/2x_k$ $x_{k+1} = (x_{k}^2+b)/2x_k$ $x_{k+1} = x_k-2x_k/\left(x^2_k+b\right)$ None of the above
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...
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3 answers
21
GATE CSE 1994 | Question: 3.4
Match the following items (i) Newton-Raphson (a) Integration (ii) Runge-Kutta (b) Root finding (iii) Gauss-Seidel (c) Ordinary Differential Equations (iv) Simpson's Rule (d) Solution of Systems of Linear Equations
Match the following items(i) Newton-Raphson(a) Integration(ii) Runge-Kutta(b) Root finding(iii) Gauss-Seidel(c) Ordinary Differential Equations(iv) Simpson's Rule(d) Solu...
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1 votes
1 answer
24
GATE CSE 1993 | Question: 01.3
Simpson's rule for integration gives exact result when $f(x)$ is a polynomial of degree $1$ $2$ $3$ $4$
Simpson's rule for integration gives exact result when $f(x)$ is a polynomial of degree$1$$2$$3$$4$
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25
GATE CSE 1987 | Question: 11b
Use Simpson's rule with $h=0.25$ to evaluate $ V= \int_{0}^{1} \frac{1}{1+x} dx$ correct to three decimal places.
Use Simpson's rule with $h=0.25$ to evaluate $ V= \int_{0}^{1} \frac{1}{1+x} dx$ correct to three decimal places.
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26
GATE CSE 1987 | Question: 11a
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.
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.
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2 votes
1 answer
28
GATE CSE 1988 | Question: 1i
Loosely speaking, we can say that a numerical method is unstable if errors introduced into the computation grow at _________ rate as the computation proceeds.
Loosely speaking, we can say that a numerical method is unstable if errors introduced into the computation grow at _________ rate as the computation proceeds.
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