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EXERCISES 1 For Exercises 1-9, find the first four nonzero terms of the Taylor series for the function about 0. 5. 1-x 6. 1+x 1. (1+x)³/2 2. Vx+1 7. V1-y 8. tan(t+/4) 3. sin(-x) 4. In(1 – x) 9. In(5+2x)

EXERCISES 1 For Exercises 1-9, find the first four nonzero terms of the Taylor series for the function about 0. 5. 1-x 6. 1+x 1. (1+x)³/2 2. Vx+1 7. V1-y 8. tan(t+/4) 3. sin(-x) 4. In(1 – x) 9. In(5+2x)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
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Fri Apr 8 8:1 7th Edition Calculus Single Variable Page 551 of 745 Q Search Figure 10.11: Convergence of the Taylor series for In(1+ x) The following theorem tells us about the relationship between power series and Taylor series; the justification involves calculations similar to those in Problem 60. Theorem 10.1: A Power Series Is its Own Taylor Series If a power series about x = a converges to f(x) for |x – a| < R, then the power series is the Taylor series for f(x) about x = a. Exercises and Problems for Section 10.2 EXERCISES 1 For Exercises 1-9, Taylor series for the function about 0. the first four nonzero terms of the 5. 1– x 6. 1. (1+x)/2 2. Vx+1 7. V1-y 8. tan(t+/4) 3. sin(-x) 4. In(1 – x) 9. In(5 + 2x) 528 Chapter 10 APPROXIMATING FUNCTIONS USING SERIES = 1+x+x² + x² + For Exercises 10–17, find the first four terms of the Taylor series for the function about the point a. 18. 1-x 19. - = 1-x+x - x' +x* – ... 1+x x² 20. In(1-x) = -x-- 10. sin x, a = 1/4 11. cos 0, a = x/4 x x* W étv
Transcribed Image Text:Fri Apr 8 8:1 7th Edition Calculus Single Variable Page 551 of 745 Q Search Figure 10.11: Convergence of the Taylor series for In(1+ x) The following theorem tells us about the relationship between power series and Taylor series; the justification involves calculations similar to those in Problem 60. Theorem 10.1: A Power Series Is its Own Taylor Series If a power series about x = a converges to f(x) for |x – a| < R, then the power series is the Taylor series for f(x) about x = a. Exercises and Problems for Section 10.2 EXERCISES 1 For Exercises 1-9, Taylor series for the function about 0. the first four nonzero terms of the 5. 1– x 6. 1. (1+x)/2 2. Vx+1 7. V1-y 8. tan(t+/4) 3. sin(-x) 4. In(1 – x) 9. In(5 + 2x) 528 Chapter 10 APPROXIMATING FUNCTIONS USING SERIES = 1+x+x² + x² + For Exercises 10–17, find the first four terms of the Taylor series for the function about the point a. 18. 1-x 19. - = 1-x+x - x' +x* – ... 1+x x² 20. In(1-x) = -x-- 10. sin x, a = 1/4 11. cos 0, a = x/4 x x* W étv
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