Exercise 29 provides an example in which an error in a partial fraction decomposition is

Chapter 12, Problem 29

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Exercise 29 provides an example in which an error in a partial fraction decomposition is not easily detected with a graphical approach. Indeed, this may be an example of a case in which, to check your partial fractions work, its easier to repeat the algebra than to experiment with numerous viewing rectangles. Decide for yourself after completing the problem.There is an error in the following partial fractiondecomposition:0. (a) Let f and g denote the two functions defined bythe expressions on the left side and the right side,respectively, in the above equation. Use a graphingutility to graph f and g, first in the standard viewingrectangle and then in the rectangle [15, 15, 5] by[0.02, 0.04, 0.02]. In this latter rectangle, note thatthe graphs do appear to be identical. (People using asoftware graphing application and looking at thecurves on a computer monitor may have a little advantagehere over those drawing the graphs on a relativelysmall graphing calculator screen.)0. (b) Find a viewing rectangle clearly demonstrating thatthe graphs of f and g are not identical.(c) Find the correct partial fraction decomposition, giventhat the form is11x 22 1x 52 1x 142 Ax 2Bx 5Cx 14GG