Quantitative Methods Answers

1.    Solve cos(x)=2x, using fixed point iteration to 5 decimal places             

Do 5 iterations.    Solve , using fixed point iteration to 5 decimal places       

 State the Euler's method formula for yk +1 in terms of tk , yk and t when approximating the solution to the initial value problem

dy = f (t, y) y(t0 ) = y0

True or false.

The global truncation error of an initial value solver can be estimated based on the Taylor series expansion of the solution of the initial value problem

1.   Add the binary numbers 1110₂ and 111₂

Approximate f(0.05) use the following data and the Newton forward-difference formula

x 0.0 0.2 0.4 0.6 0.8

f(x) 1.00000 1.22140 1.49182 1.82212 2.22554

b. use the Newton backward-difference formula to approximate f(0.65)

c.Use stirlings formula to approximate f(0.43).

6)                 If f(x) takes the values -21, 15, 12 and 3 respectively when x assumes the values -1, 1, 2 and 3, find the polynomial which approximates f(x).

A rm's total cost function is given as T C = 4 + 8Q − Q 2 , and total revenue as T R = 50Q − 4Q 2 , where Q is the number of units produced and sold (in thousands). How many units should be produced to maximize prot?