Numerical Solution of Equation

The approximation to a root of the equation $x^2+x-1=0$ in the interval $\left(0,1\right)$ by applying method of false position one time, will be:

The order of convergence of Newton Raphson method is

At which point the iterations in the Newton Raphson method are stopped?

In Newton Raphson method if the curve $f\left(x\right)$ is constant then _____

If $f\left(x\right)=x^2–153=0$ then the iterative formula for Newton Raphson Method is given by _____

The Iterative formula for Newton Raphson method is given by _____

The Newton-Raphson method of finding roots of nonlinear equations falls under the category of which of the following methods?

Rate of convergence of the Newton-Raphson method is generally_____

Find the approximated value of $x$ till $4$ iterations for $e^{-x}=3\log \left(x\right)$ using Bisection Method.

Use Bisection Method to find out the root of $x–\sin x–0.5=0$ between $1$ and $2$.

A function $f\left(x\right)$ is given as $e^{-x}\times \left(x^2+5x+2\right)+1=0$. Let $a=0$ and $b=-1$. Find the root between $a$ and $b$ using Bisection Method.

A function is given by $x–e^{-x}=0$. Find the root between $a=0$ and $b=1$ by using Bisection method.

Find the root of $x^4-x-10=0$ approximately upto $5$ iterations using Bisection Method. Let $a=1.5$ and $b=2$.

Using Bisection method find the root of $\cos \left(x\right)-x\times e^x=0$ with $a=0$ and $b=1$.

If $\alpha ,\beta ,\gamma$ are the roots of $8x^3-4x^2+6x-1=0$, find the equation $\alpha +1/2,\beta +1/2$ and $\gamma +1/2$.

If one root of the equation $f\left(x\right)=0$ is near to $x_0$, then the first approximation of this root as calculated by Newton Raphson method is the abscissa of the point, where the following straight line intersects the x-axis"

In solving ordinary differential equation $y\text{'}=2x, y\left(0\right)=0$ using Euler's method, the iterate $y_n, n\in N$ satisfy

If $f\left(0\right)=3, f\left(1\right)=5, f\left(3\right)=21$, then the unique polynomial of degree $2$ or less using Newton divided difference interpolation will be: 

One real root of a polynomial $P\left(x\right)=x^3-x-1$ lies in the interval $\left[1,2\right]$ and bisection method is used to find its value, the minimum number of interations required to achieve accuracy up to two decimal points is

The $2^{\mathrm{nd}}$ approximation to a root of the equation $x^2-x-1=0$ in the interval $\left(1,2\right)$ by Bisection method will be: