MAD 3401 Study Guide - Midterm Guide: Bisection Method, Approximation Error, Roundoff
3 Jun 2015
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For every , - there exists a number ( ) between xo and x with: Let f(x) = x3 : find the second taylor polynomial p2(x) about x0 = 0, find r2(0. 5) and the actual error in using p2(0. 5) to approximate f(0. 5). Example b0 10000000011 1011100100010000000000000000000000000000000000000000: , indicates the number is positive. Suppose that p* is an approximate of p. Chopping the first m digits of the mantissa are retained, simply chopping off the remainder. Rounding the computer chooses the closest number that is representable by the computer. = 10-1: a. r. is strongly dependent on the magnitude of x, r. e is a measure of the number of significant digits of x that are correct. Find the largest interval in which p* must lie to approximate p with relative error at most 10-4 for each value of p ( ). Let * + and * + be the sequences that satisfy:
