Quantitative Methods Answers

To approximate the value of f'''(xk), the following formulas are used
f'''k =1/h^3[ fk+3 −3 fk+2 +3 fk+1 − fk]
f'''k =1/2h3[ fk+2 −2 fk+1 +2 fk−1 − fk−2]
Which formula do you find more accurate, and why?

Find the approximate area under the curve y= sqrt{x^2+1} on the interval [0,1] using the trapezoid method and 5 subintervals.

Use a numerical solver and Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05.


y' = x^2 + y^2, y(0) = 3; y(0.5)


y(0.5) ≈ _______ (h = 0.1)

y(0.5) ≈ _______ (h = 0.05)

Use a numerical solver and Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05.


y' = x2 + y2, y(0) = 3; y(0.5)


y(0.5) ≈ _________ (h = 0.1)

y(0.5) ≈ _________(h = 0.05)

Use a numerical solver and Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05.


y' = x2 + y2, y(0) = 3; y(0.5)


y(0.5)≈ ________ (h = 0.1)

y(0.5)≈ ________ (h = 0.05)

The operations manager of a large production plant would like to estimate the average amount of time workers take to assemble a new electronic component. After observing a number of workers assembling similar devices, she guesses that the standard deviation is 6 minutes. How large a sample of workers should she take if she wishes to estimate the mean assembly time to within 20 seconds? Assume that the confidence level is to be 99%.

Using Bessel’s difference interpolation formula, to compute the value of y(5) for the

following data given below:

x: 0 4 8 12

y: 14.27 15.81 17.72 19.96

solve for t in the following equation by means of linear interpolation

( 1+ t )^10 - 1/ t = 25

From the following data find f'(5).

x= 1 3 4 6

F(x)= 14 2 8 9