3. Consider the function f(x) = r - 1+x 1- a. Explain why, when evaluated in a floating point system, this expression is subject to a large increase of its relative error (catastrophic cancelation) when x is a very small number. b. Find a formula that is equivalent to the one above in exact mathematics and that does not suffer of catastrophic cancelation.

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Q: | (1 – a*)dæ (1 — а?) а

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