Recent questions in Numerical Methods

Newton-Raphson method for solving algebraic equations is based onTaylor seriesFourier seriesLaurent seriesPower series

The exact solution of $\int_{0}^{4} \frac{d x}{1+x}$ is represented as $n$.If $m$ represents numerically evaluated value of the above integral using Trapezoidal rule by c...

The values of a function $f$ obtained for different values of $x$ are shown in the table below.$x$00.250.50.751.0$f(x)$0.92.01.51.80.4Using Simpson's one-third rule,$\int...

The initial value problem$$\frac{d y}{d t}+2 y=0, \quad y(0)=1$$is solved numerically using the forward Euler's method with a constant and positive time step of $\Delta t...

A solid part (see figure) of polymer material is to be fabricated by additive manufacturing $\text{(AM)}$ in square-shaped layers starting from the bottom of the part wor...

Value of $\int_{4}^{5.2} \ln x\: dx$ using Simpson’s one-third rule with interval size $0.3$ is$1.83$$1.60$$1.51$$1.06$

Find the positive real root of $x^3-x-3=0$ using Newton-Raphson method. lf the starting guess $(x_{0})$ is $2,$ the numerical value of the root after two iterations $(x_{...

For the integral $\displaystyle \int_0 ^{\pi/2} (8+4 \cos x) dx$, the absolute percentage error in numerical evaluation with the Trapezoidal rule, using only the end poin...

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 __________.

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$$1.248$$...

Evaluation of $\int_2^4 x^3 dx$ using a $2$-equal-segment trapezoidal rule gives a value of _______

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...

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 ______

Maximise $Z=5x_{1}+3x_{2}$subject to$\begin{array}{} x_{1}+2x_{2} \leq 10, \\ x_{1}-x_{2} \leq 8, \\ x_{1}, x_{2} \geq 0 \end{array}$In the starting Simplex tableau, $...

$P(0, 3), Q (0.5, 4)$ and $R(1, 5)$ are three points on the curve defined by $f(x)$. Numerical integration is carried out using both Trapezoidal rule and Simpson's rule w...

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$...

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...

Numerical integration using trapezoidal rule gives the best result for a single variable function, which islinearparaboliclogarithmichyperbolic

Maximize $Z = 15X_1 + 20X_2$ subject to $$\begin{array}{l} 12X_1 + 4X_2 \geq 36 \\ 12X_1 − 6X_2 \leq 24 \\ X_1, X_2 \geq 0 \end{array}$$The above linear programming prob...

Gauss-Seidel method is used to solve the following equations (as per the given order):$x_1+2x_2+3x_3=5$$2x_1+3x_2+x_3=1$$3x_1+2x_2+x_3=3$Assuming initial guess as $x_1=x_...