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Exercise 1.36: Modify fixed-point so that
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it prints the sequence of approximations it generates, using the newline
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and display primitives shown in Exercise 1.22. Then find a
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solution to
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x
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x
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=
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1000
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by finding a fixed point of
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x
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↦
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log
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(
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1000
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)
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/
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log
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(
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x
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)
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. (Use Scheme’s primitive log
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procedure, which computes natural logarithms.) Compare the number of steps
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this takes with and without average damping. (Note that you cannot start
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fixed-point with a guess of 1, as this would cause division by
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log
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(
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1
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)
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=
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0
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.)
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