Recent questions and answers in Numerical Methods

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The minimum number of equal length subintervals needed to approximate $\int_{1}^{2}xe^xdx$ to an accuracy of atleast (10^(-6))/3 using trapezoidal rule is __________.
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The evaluation of the definite integral $\int ^{1.4}_{ – 1}x \mid x \mid dx$ by using Simpson’s $1/3^{rd}$ (one - third) rule with step size $h=0.6$ yields$0.914$$1.2...
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The problem of maximizing $z=x_1-x_2$ subject to constraints $x_1+x_2 \leq 10, \: x_1 \geq 0, x_2 \geq 0$ and $x_2 \leq 5$ hasno solutionone solutiontwo solutionsmore tha...
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The minimum value of $3x+5y$ such that$3x+5y \leq 15$$4x+9y \leq 18$$13x+2y \leq 2$$x \geq 0, \: y \geq 0$ is ______
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The root of the function $f(x) = x^3+x-1$ obtained after first iteration on application of Newton-Raphson scheme using an initial guess of $x_0=1$ is$0.682$$0.686$$0.750$...
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The error in numerically computing the integral $\int_{0}^{\pi }(\sin x+\cos x)dx$ using the trapezoidal rule with three intervals of equal length between $0$ and $\pi$ i...
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Numerical integration using trapezoidal rule gives the best result for a single variable function, which islinearparaboliclogarithmichyperbolic
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Solve the equation $x=10\cos(x)$ using the Newton-Raphson method. The initial guess is $x=\pi /4$. The value of the predicted root after the first iteration, up to second...
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Newton-Raphson method is used to find the roots of the equation, $x^3+3x^2+3x-1=0$. If the initial guess is $x_0=1$, then the value of $x$ after $2^{nd}$ iteration is ___...
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Simpson’s $\dfrac{1}{3}$ rule is used to integrate the function $f(x)=\dfrac{3}{5}x^2+\dfrac{9}{5}$ between $x = 0$ and $x=1$ using the least number of equal sub-interv...
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Consider an objective function $Z(x_1,x_2)=3x_1+9x_2$ and the constraints$x_1+x_2 \leq 8$$x_1+2x_2 \leq 4$$x_1 \geq 0$ , $x_2 \geq 0$The maximum value of the objective...
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The value of $\int_{2.5}^{4} \ln(x)dx$ calculated using the Trapezoidal rule with five subintervals is _______
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The best approximation of the minimum value attained by $e^{-x}\sin(100x)$ for $x\geq 0$ is _______
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Using the trapezoidal rule, and dividing the interval of integration into three equal subintervals, the definite integral $\int_{-1}^{+1} \mid x \mid dx$ is _____
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Match the CORRECT pairs:$\begin{array}{llll} & \text{Numerical Integration Scheme} & & \text{Order of Fitting Polynomial} \\ P. & \text{Simpson's 3/8 Rule} & 1. & \text{F...
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