help with problem 25 please, write it on paper step by step in detail, test end points(I confuse on how to do this step) 3.4.5.6.2.QUICK CHECK 5 Verify that the powerseries in Example 5b does not con-verge at the endpoints x =±1.<12. ΣSECTION 11.2 EXERCISESReview QuestionsWrite the first four terms of a power series with coefficients Co, C1, C₂, 15, sinx1.and c3 centered at 0.Write the first four terms of a power series with coefficients Co, C1, C2,and c3 centered at 3.What tests are used to determine the radius of convergence of apower series?= 2 ( x +Explain why a power series is tested for absolute convergence.Do the interval and radius of convergence of a power serieschange when the series is differentiated or integrated? Explain.What is the radius of convergence of the power series Σc, (x/2)*if the radius of convergence of Eck xk is R?What is the interval of convergence of the power series Σ(4x)^?7.8. How are the radii of convergence of the power series Eckx andΣ(-1)* cxk related?Basic Skills9-28. Interval and radius of convergence Determine the radius ofconvergence of the following power series. Then test the endpoints todetermine the interval of convergence.9. Σ(2x) *(x - 1)*k!2Σk=0 2k + 1This power series is the difference of two power series, both of which convergethe interval x < 1. Therefore, by Theorem 11.4, the new series also convergesIf you look carefully, every example in this section is ultimately based on the pRelated Exercises|x) < 1.ric series. Using this single series, we were able to develop power series formanyfunctions. Imagine what we could do with a few more basic power series. The followsection accomplishes precisely that end. There, we discover basic power series for allstandard functions of calculus.10. (2x)k!13. Σ(kx)*11. Σ(x - 1)kk3x 2k+114. Σk! (x - 10)*+Σ15. Σ sin¹ (+) 16. ²¹(x-3)*k18. Σ(-1)-19. Σk²x2k21. Σ k!24. ΣΣ(-1)27. Σ29. f(3x)5k25. Σ (k + 1) kk20 *(2k + 1)!28. Σ(-1)*.29-34. Combining power series Use the geometric series31. h(x) =33. p(x) ==2kf(x)Sumination notation22. Σk (x - 1)k(x - 1)kkk=11 - 3x2x³1 - x4x¹21- x111X=17.x3k27k20. Σ(-1)(xx²k+13k-123. Σ26. Σto find the power series representation for the following functiontered at 0). Give the interval of convergence of the new series.30. g(x)for x < 1,+334. f(-4x)To findGive the35. S37. h39. F1- x132. f(x³)=₁-x²)1=(-2)* (x+3)3k+141-4serieingof c2411 + 4x41

We have to find the radius and interval of convergence. We will use Ratio Test to find the radius…

Answered: help with problem 25

help with problem 25

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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