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88 lines
1.6 KiB
88 lines
1.6 KiB
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Exercise 2.13: Show that under the assumption of
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small percentage tolerances there is a simple formula for the approximate
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percentage tolerance of the product of two intervals in terms of the tolerances
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of the factors. You may simplify the problem by assuming that all numbers are
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positive.
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After considerable work, Alyssa P. Hacker delivers her finished system.
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Several years later, after she has forgotten all about it, she gets a frenzied
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call from an irate user, Lem E. Tweakit. It seems that Lem has noticed that
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the formula for parallel resistors can be written in two algebraically
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equivalent ways:
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R
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1
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R
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2
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R
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1
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+
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R
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2
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and
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1
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1
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/
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R
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1
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+
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1
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/
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R
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2
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.
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He has written the following two programs, each of which computes the
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parallel-resistors formula differently:
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(define (par1 r1 r2)
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(div-interval
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(mul-interval r1 r2)
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(add-interval r1 r2)))
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(define (par2 r1 r2)
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(let ((one (make-interval 1 1)))
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(div-interval
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one
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(add-interval
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(div-interval one r1)
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(div-interval one r2)))))
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Lem complains that Alyssa’s program gives different answers for the two ways of
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computing. This is a serious complaint.
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