module5_MAT-232-jan12 - MAT232:CALCULUSII ,Part2 TOPICS

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MAT­232: CALCULUS IIModule 5—Infinite Series, Part 2TOPICSModule 5 covers the following topics:finding Maclaurin polynomials of transcendental functionsapproximating a function at a particular point using a Taylor polynomialfinding the error of the approximation using the Lagrange form of the remainderapproximating the function at a point to any desired level of accuracyfinding Maclaurin and Taylor polynomials to any degreetesting the endpoints of the interval of convergence for absolute and conditional convergenceusing the fact that within the open interval of convergence, series can be differentiated andintegrated term by termintegrating and differentiating a series term by termYou may have wondered how it is possible for calculators to come up with values of transcendentalfunctions. For example, how is it possible to program a value for e4? The answer is that a Taylor polynomialis used to approximate that value. After all, polynomials only require sums of products of numbers that canreadily be programmed. Furthermore the Lagrange form of the remainder assures us of the level of accuracyrequired. Thus, the applications of Maclaurin and Taylor polynomials have an impact on all of us.STUDY MATERIALSTextbook ReadingsStudy sections 8.6, 8.7, and 8.8 in the course textbook. Then read the TechnicalCommentary topics given below.Technical CommentaryRead the following brief commentary topics for further explanations and notes on the material covered in thismodule. Following the commentary are video tutorials and suggested Self­Check Exercises. Be sure to workthrough these practice exercises to help solidify the skills learned in the module and to prepare for themodule­ending written assignment.

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