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Unformatted text preview: ChE 2120 Exam 2 November 8, 2004 ‘ (I) (40 pts) Consider the following data, from the function y = f(x)‘ a. (20 pts) Fit a second order polynomial to this data using least squares
regression.
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21" ’4‘ +331 i’ b. (5 pts) Compute the integral of y(x) from x = l to x = 3 using the (" trapezoidal rule. C + 2 32. __ .3 2 __ (sailUrr 2(3) Hr”) I ’39,. : 5 c. (5 pts) Compute the integral of 3100 using Simpson’s 1/3 rule. II ( b’Q) z 3
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3 5’? d. (5 pts) Anglytically integrate the polynomial ﬁt from Part a. K I "a Yrg+£7¢+('2)'x?_cfar ” '27 .
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we ﬁrs } Of CQV‘ C2,) I... f” M (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. _
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b. (10 pts) Compute the derivative of the polynomial ﬁt, and evaluate it at each of the three points. . (15 pts) Use the Golden section method to ﬁnd the maximum of the
polynomial ﬁt. Perform three iterations. at“ .9 we d. (5 pts) Explain how these results compare and why. WT ‘ .
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7 W Mains cl \ if [viv K\J~.Cx}—L\/\LA {wk w {p.{’ C {'1 {W £13 0‘ i n... (3) (10 pts) Concentration data was taken at timeupojntéhfor the polymerization
reaction 7—"— xA+yBﬁAxBy 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. (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 (x0,yo) =
(1,1). b. (5 pts) Sketch 3 iterations of the steepest ascent method, beginning at 010,510) =
(1,1). ...
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This note was uploaded on 05/10/2008 for the course CHBE 2120 taught by Professor Gallivan during the Summer '07 term at Georgia Institute of Technology.
 Summer '07
 Gallivan

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