Numerical Methods

Consider the following recursive iteration scheme for different values of variable P with the initial guess $x_1 = 1$: $x_{n+1} = \frac{1}{2} (x_n + \frac{P}{x_n})$, $n = 1, 2, 3, 4, 5$ For $P = 2$, $x_5$ is obtained to...

The value of $\int_0^1 e^x dx$ using the trapezoidal rule with four equal subintervals is

A continuous function f(x) is defined. If the third derivative at $x_i$ is to be computed by using the fourth order central finite-divided-difference scheme (with step length = h), the correct formula is

The quadratic equation $2x^2-3x+3=0$ is to be solved numerically starting with an initial guess as $x_0 = 2$. The new estimate of $x$ after the first iteration using Newton-Raphson method is _________