Exam 2 Fall 2004

# Exam 2 Fall 2004 - d(5 pts Explain how these results...

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ChE 2120 Exam 2 November 8, 2004 (1) (40 pts) Consider the following data, from the function y = f(x) x y 1 4 2 5 3 -1 a. (20 pts) Fit a second order polynomial to this data using least squares regression. b. (5 pts) Compute the integral of y(x) from x = 1 to x = 3 using the trapezoidal rule.

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c. (5 pts) Compute the integral of y(x) using Simpson’s 1/3 rule. d. (5 pts) Analytically integrate the polynomial fit from Part a. e. (5 pts) Explain how these results compare and why.
(2) (40 pts) Again consider the data from Problem 1. a. (10 pts) Compute the derivatives at each of the three points using a finite difference method. Explain why you chose the method(s) that you did. b. (10 pts) Compute the derivative of the polynomial fit, and evaluate it at each of the three points. c. (15 pts) Use the Golden section method to find the maximum of the polynomial fit. Perform three iterations.

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Unformatted text preview: d. (5 pts) Explain how these results compare and why. (3) (10 pts) Concentration data was taken at 15 time points for the polymerization reaction x A + y B → A x B y We assume the reaction occurs via a complex mechanism consisting of many steps. Several models have been hypothesized and the sum of the squares of the residuals had been calculated for the fits of the models of the data. The results are shown below. Which model best describes the data (statistically)? Explain your choice. Model A Model B Model C S r 135 90 72 Number of model parameters fit 2 3 6 (4) (10 pts) Find the maximum of z = f(x,y). Assume that the function varies smoothly between the contours. a. (5 pts) Sketch 3 iterations of the univariate method, beginning at (x ,y ) = (1,1). b. (5 pts) Sketch 3 iterations of the steepest ascent method, beginning at (x ,y ) = (1,1)....
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Exam 2 Fall 2004 - d(5 pts Explain how these results...

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