Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
C-108 Appendix C<br />
MINI PROJECT<br />
Checking a Partial Fraction Decomposition<br />
3<br />
The partial fraction decomposition for the expression<br />
the form<br />
x(x 17)(x 2 13)<br />
A<br />
x B<br />
x 17 Cx D<br />
x 2 13<br />
Suppose that a classmate of yours worked out the following values for the<br />
constants:<br />
A 3<br />
221 , B 3<br />
5135 , C 51<br />
3925 , D 3<br />
302<br />
has<br />
(a) Use a graphing utility to check this decomposition, as in the text, after<br />
Example 1. Unlike Example 1, however, not all of the constants given here<br />
are correct. Yet, initially, no difference in the two graphs is apparent. Can<br />
you find a viewing rectangle that clearly demonstrates that there must be<br />
an error in the decomposition? (It’s certainly not the standard viewing rectangle.)<br />
Can you think of a simple nongraphical way to check for the presence<br />
of an error (short of rederiving the entire decomposition from<br />
scratch)?<br />
(b) Determine correct values for the constants A, B, C, and D. If you have<br />
access to software or a graphing utility that computes partial fraction<br />
decompositions, use that. There are also interactive partial fraction calculators<br />
available on-line. Try using a search engine to locate “partial fraction<br />
expansion” or “partial fraction calculator.” At the time of this writing,<br />
for example, one such calculator (developed by Professor Philip S. Crooke<br />
at Vanderbilt University) could be accessed from the web page http://MSS<br />
.math.vanderbilt.edu. Finally, if neither of these options works out for you,<br />
use the methods of this section to find the decomposition.
Change language