Quantitative Methods Answers

Given the following data, estimate the value of f(5) using
i) Lagrange’s interpolation
ii) Newton’s divided difference interpolation
x 1 4 6 7 10
f(x) -3 9 10 9 8

Using simulated business cases illustrate the following terms as used in linear cost volume profit analysis. 1. Market Equilibrium. 2. The margin of safety

Set up the iteration method in matrix form for the following system of linear equations :
3x1 - x4 = 1
4x1 -x2 + X3 =4
X1 + 2x3 =1
-x1 -x2 -x4 = 2
Further determine whether the method converges or not.

Find the minimum number of intervals required to evaluate int (e^(-x^2 +1))dx with an accuracy of 0.5 × 10^(-4) , by using Trapezoidal rule.

Calculate the fourth degree Taylor polynomial about x0 = 0.5 for the function f(x) = sin^(-1) √x

Using the classical fourth order Runge-Kutta method, find the approximate value of y(0.6) for the initial value problem dy/dx = sin xy ; y(0) =1 with the step size h =0.2

Perform iterations of Newton-Raphson method to approximate a root of the equation f(x) = x^4 -x^3 +x -1 =0 , until the roots at successive iterations are closer than 10^(-5). How many iterations do you need for this much accuracy.

bureau of labor statistics want to use statistics to determine whether there is a difference between 2 countries on some measure of labor or between time periods of one country.hourly compensation in US dollars for manufacturing production workers in country A in 2015 and 2019 were $25.96 and $28.29 respectively.Hourly compensation for country B were $19.26 in 1995 and $23.89 in 2004.actual hours worked in country A in 2015 were 36.1and 35.5 in 2019.country B 37.1 in2015 and 35.9 in 2019. was the hourly labor cost higher in country A in 2019 than country B in 2019?

Perform 6 iteration to find zero of the equation: x+3=e^x using bisection algorithm. How many steps of the algorithm are needed to compute toot of the equation?

To approximate the value of f'''(Xk), the following formulas are used:
f'''k =[ fk+3 −3 fk+2 +3 fk+1 − fk]÷h^3

f'''k =[ fk+2 −2 fk+1 +2 fk−1 − fk−2]÷2h^3
Which formula do you find more accurate, and why?