Module 22 - Answers Lesson 1 Answer 1 22.1.1 The graphs appear to coincide approximately on the interval (-1/2, 1/2).  Answer 2 22.1.2   The graph of y = 1/(1 - x) is in "thick" style and the graph of the tenth-degree partial sum y = 1 + x + x2 + ... + x10 = (xn, n, 0, 10) is in line style.   Answer 3 22.1.3 The graphs appear to converge to y = sin x around x = 0.  Answer 4 22.1.4   Answer 5 22.1.5   The graphs are shown in [-10, 10] x [-10, 10] and [0, 10] x [0, 1000] viewing windows.  As more terms are added, the interval where the partial sums are approximately the same as ex widens. The interval of convergence for the infinite power series is (– , )  Lesson 2 Answer 1 22.2.1 The quadratic polynomial is 0.01847 greater than the actual value of y = ex when x = -0.5 and 0.02372 less than the actual value of y = ex when x = 0.5.  Answer 2 22.2.2    Answer 3 22.2.3   The graphs of y = ln(1 + x) (thick) and the 5th-order polynomial (line) are shown in a [-7.9, 7.9] x [-3, 3] window.   Lesson 3 Answer 1 22.3.1 Near .  Answer 2 22.3.2 Near .  Answer 3 22.3.3  The derivative of the fifth-degree Taylor polynomial centered at 1 for y = ln x is equal to the fourth-degree Taylor polynomial centered at 1 for . This seems reasonable because .  Answer 4 22.3.4 The derivative of the fifth- degree Maclaurin polynomial for y = sin x should be equal to the fourth- degree Maclaurin polynomial for y = cos x.  Self Test Answer 1 Answer 2 The graphs are shown in a [-2, 2] x [-2, 2] window. The interval of convergence appears to be (-1,1). Answer 3 Answer 4   Answer 5 The 5th-order Maclaurin polynomial for  ©Copyright 2007 All rights reserved. | Trademarks | Privacy Policy | Link Policy