Engineering 6 Midterm Solutions, Fall 2009
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session on Wednesday, November 18. Regrades will only be considered in cases where it looks like
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Exam Version A (blue and white copies)
Problem 1 (22 points).
(a) (6 points)
x = linspace(-2,39,873);
%Define values of x in row vector
a = [7
0
13
-9
16];
%Define polynomial coefficient vector
A = polyval(a,x);
%Calculate values
(b) (6 points)
x = linspace(-2,39,873);
%Okay to leave this out if have it in part (a)
A = 7*x.^4 + 13*x.^2 – 9*x + 16;
%Note: only two dot operators needed.
(c) (8 points)
h = [2
0
0
3
0
0
0
-8];
%Define polynomial coefficient vectors
g = [12
5
4
15];
[c r q] = residue(h,g);
%Get residues (c), roots (r), and quotient coeffs (q)
Note: Okay to write [c,r,q] = etc.
The ratio H/G is an improper rational function, so the general form of the result will be (assuming no
repeated roots)
n
n
r
x
c
r
x
c
r
x
c
x
Q
x
G
x
H
2
2
1
1
)
(
)
(
)
(
where Q(x) is the quotient polynomial and the rest of the terms are the partial fraction expansion. In the
Matlab code, the variable q will contain the coefficients of Q(x), the variable c will contain the c’s
(residues), and the variable r will contain the r’s (roots of the denominator polynomial G(x)).
(d) (2 points)
There would be 3 terms in the partial fraction expansion, because the denominator polynomial G(x) is
third order, and thus has three roots.

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