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2. Find the Taylor polynomial of each of the following functions by manipulating the Taylor polynomials for other functions. You may use summation notation if you wish, otherwise, be sure to include at least the first 4 non-zero terms of the series. 1. (a) In(x) about x = 1. (b) about x = 1. (Hint: Use your answer to 1(c)!) (c) x°e-4 about x = 0. (d) x sin(x) about x = 0.

2. Find the Taylor polynomial of each of the following functions by manipulating the Taylor polynomials for other functions. You may use summation notation if you wish, otherwise, be sure to include at least the first 4 non-zero terms of the series. 1. (a) In(x) about x = 1. (b) about x = 1. (Hint: Use your answer to 1(c)!) (c) x°e-4 about x = 0. (d) x sin(x) about x = 0.

Advanced Engineering Mathematics
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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Please do a, b, c, d and explain how specifically you’re supposed to manipulate existing Taylor polynomials for other functions to solve these questions.
2. Find the Taylor polynomial of each of the following functions by manipulating the Taylor polynomials for other functions. You may use summation notation if you wish, otherwise, be sure to include at least the first 4 non-zero terms of the series. 1 (a) In(x) about x = 1. (b) about x = 1. (Hint: Use your answer to 1(c)!) (c) x³e¬4 about x = 0. (d) x sin(x) about x = 0. (e) 2 sin(3x) about x = 0. (f) about x = 1 using the Taylor polynomial of In(x) about x = 1. 1 (g) about x = 1 using the Taylor polynomial of about x = 0. r.
Transcribed Image Text:2. Find the Taylor polynomial of each of the following functions by manipulating the Taylor polynomials for other functions. You may use summation notation if you wish, otherwise, be sure to include at least the first 4 non-zero terms of the series. 1 (a) In(x) about x = 1. (b) about x = 1. (Hint: Use your answer to 1(c)!) (c) x³e¬4 about x = 0. (d) x sin(x) about x = 0. (e) 2 sin(3x) about x = 0. (f) about x = 1 using the Taylor polynomial of In(x) about x = 1. 1 (g) about x = 1 using the Taylor polynomial of about x = 0. r.
(i) xe2 about x = 0 using the Taylor polynomial of e about x = 0 and multiplying. (j) xe about x = 0 using the Taylor polynomial of e about r = 0 and differentiating. Final Answers: (-1)" -(z-1)까! 1 (a) In(r) = (r – 1) – (7 – 1)° +(r – 1) - (r – 1)* +... . n+1 n=0 (b) =1-(-1)+- 1) -(-1)° +.. 3 16 - 1)° +... (Summation notation in (b) is more than we would expect.) 32 (c) x³e-1 = r³ 4x* + 8x° - + 3 2. Σ (-1)"4"r"+3 ... n! n=0 1 (d) x sin(x) = x² . 1 (-1)"22n+2 (2n + 1)! 1 +... = | 120 5040 n=0 249
Transcribed Image Text:(i) xe2 about x = 0 using the Taylor polynomial of e about x = 0 and multiplying. (j) xe about x = 0 using the Taylor polynomial of e about r = 0 and differentiating. Final Answers: (-1)" -(z-1)까! 1 (a) In(r) = (r – 1) – (7 – 1)° +(r – 1) - (r – 1)* +... . n+1 n=0 (b) =1-(-1)+- 1) -(-1)° +.. 3 16 - 1)° +... (Summation notation in (b) is more than we would expect.) 32 (c) x³e-1 = r³ 4x* + 8x° - + 3 2. Σ (-1)"4"r"+3 ... n! n=0 1 (d) x sin(x) = x² . 1 (-1)"22n+2 (2n + 1)! 1 +... = | 120 5040 n=0 249
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