In Simpson's 1/3 Rule, the curve y = f(x) is assumed to be a:
The equation sin x + eˣ = 0 is:
Given the equation x⁴ − x − 10 = 0, the root of the equation lies between:
The process of numerical integration is called:
Given the equation x³ − x − 10 = 0, the root of the equation lies between:
The Newton–Raphson method is also called the:
To find the roots of the equation f(x) = 0, the Newton–Raphson iterative formula is:
The equation of the directrix of the parabola y² − 6y − 6x + 21 = 0 is:
Iteration is also called a:
Taking x₀ = 0 and x₁ = 1 as the initial guesses, the value of x after the first iteration for the equation x = e⁻ˣ using the Regula Falsi method is:
In Simpson's 1/3 Rule, if the interval width is reduced by a factor of 3, the truncation error is reduced to:
The equation f(x) = x² − 4 = 0 is solved using the Newton–Raphson method. Considering the initial approximation x₀ = 6, the value of x₁ is:
The first approximation to a real root of the equation x³ − 2x² − 2 = 0 using the Regula Falsi method in the interval [2, 3] is:
To decrease the number of iterations in the Newton–Raphson method:
In the Newton–Raphson method, the equation of the tangent at a point is given by:
In the Newton–Raphson method, if the curve f(x) is constant, then:
The points where the Newton–Raphson method fails are called:
Find the approximate value of x after the first iteration using the Bisection Method for the equation x³ − 4x + 9 = 0 taking a = −3 and b = −2.
The Newton–Raphson method is applicable to:
The convergence of which of the following methods depends on the initial assumed value?
