3. Consider the function f(x) = r - : 1+x 1-x a. Explain why, when evaluated in a floating point system, this expression is subject to a large increase of its relative error (catastrophic cancelation)...

Extracted text: 3. Consider the function f(x) = r - : 1+x 1-x 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.