State whether the following statements are True or False. If True, explain why, and if False, give a counter- example (an example that fits the premises but not the conclusion): (a) If Eko(ak + bk) converges, then Σko ak and Eko bk converge individually as series. k=0 (b) The Taylor polynomial of (ƒ+g)(x) centered at x = a is the sum of the Taylor polynomial of f(x) centered at x =a and the Taylor polynomial of g(x) centered at x = a. (c) The Taylor polynomial of f(x) centered at x = a +b is the sum of the Taylor polynomial of f(x) centered at x = a and the Taylor polynomial of f(x) centered at x = b. (d) Let f(x) be a degree 3 polynomial. Then the Taylor series of f(x) is also a polynomial of degree 3.

State whether the following statements are True or False. If True, explain why, and if False, give a counter- example (an example that fits the premises but not the conclusion): (a) If Eko(ak + bk) converges, then Σko ak and Eko bk converge individually as series. k=0 (b) The Taylor polynomial of (ƒ+g)(x) centered at x = a is the sum of the Taylor polynomial of f(x) centered at x =a and the Taylor polynomial of g(x) centered at x = a. (c) The Taylor polynomial of f(x) centered at x = a +b is the sum of the Taylor polynomial of f(x) centered at x = a and the Taylor polynomial of f(x) centered at x = b. (d) Let f(x) be a degree 3 polynomial. Then the Taylor series of f(x) is also a polynomial of degree 3.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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