Quantitative Methods Answers

The following table of values of f(x) is given:
x →0.25 0.30 0.35
f(x)→1.25 1.90 1.68

Compute f'(x) at x=0.30 using an O(h²) formula.

Perform three iterations of the inverse power method to obtain the smallest eigenvalue in magnitude of the matrix [{2,5},{3,6}].
Take appropriate initial approximation to the eigenvector.

Find by Newton's method the root of the equation
xlog_(10 )x=4
near x=6 correct to 3 decimal places of digits.

Solve x^3+x^2−10x+1=0 for the root lying between 0 and 1 by the method of false position. Perform two iterations only.

a sales girl gave a change of 1.15 to a customer instead of 1.25. calculate her percentage error

For the equation y = 5 + 4x^2 + 5x^3
(a) Find the equation for the linear approximation when x = 3.
(b) Find the equation for the quadratic approximation, also when x = 3.

For the equation y = 2 + 3 + 4x^2 + 5x^3
(a) Find the equation for the linear approximation when x = 3.
(b) Find the equation for the quadratic approximation, also when x = 3.

For the equation y = 2 + 3 + 4x2 + 5x3
(a) Find the equation for the linear approximation when x = 3.
(b) Find the equation for the quadratic approximation, also when x = 3.

Write abstract of Runge Kutta Method and Runge Kutta Fehlberg Method.

Define local truncation error.