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# Review Sheet for MATH 129 with Professor Glickenstein at UA

Marketplace > University of Arizona > Review Sheet for MATH 129 with Professor Glickenstein at UA

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COURSE
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KARMA
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This 2 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Arizona taught by a professor in Fall. Since its upload, it has received 15 views.

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Date Created: 02/06/15
Chapter 9 and 10 Review 1 Consider the series 2200 an State if the following are true or false Be sure to justify your answers a If limnnoo 220 an S then 2200 an S b If limnnoo an 0 then the series converges c If the series is a geometric series and limnnoo an 0 then the series converges d If the series is alternating and limnnoo an 0 then the series converges e If limngw ag1 l 1 then the series converges f If limnnoo an lt 1 then the series converges g If an lt then the series converges h lf lanl S i then the series converges i If lanl 2 i then the series diverges lf 220 an diverges and 220 bn diverges7 then 2200 an bn diverges k If 220 lanl diverges then 2200 an diverges 1 If the power series 220 bn at 7 4 has radius of convergence 5 then the series converges for 75 S at S 5 2 Find the Taylor series for the following functions and give the radius of convergence and the interval of convergence a sin13 at 350 b cos3x at 350 c 3551 71 at 350 d i at ac 1 e arctan at ac 0 f ln7ac at at 71 gx421atac0 hx421atac2 f atx0 3 Compute the following 20 3 Zno3n b 2212 G 0 222 Q 4 Find if the following series converge or diverge 2 3 2201 b 2201 C 2200 n21 d 2201 9Z10 110 3 g hgt1quot313 0222 1711711m k 7 7 g7 1 9 27 1 1 1 Zoo 1 E E 39 39 39 m 711 qn52n 1 0112 013 014 015 b 221 W c17gii107 d 1x2x4x6x8 7 1 2745 221 7 f 220 Un 6 Estimate the errors of the following approximations a 1 7 7 i as an approximation to 221 71 b 1 7 g as an approximation to cos 05 7 What degree Taylor polynomial can we use to approximate the following to 5 decimal places a sin1 b W note that 05 lt 1 lt 1 c 7T 4arctan1 8 Compute the radius of convergence for the following power series Also give the interval of convergence if possible a 221 as 7 a b 220 as 1 c 223 n 73 W a 2 Hquot x 4 110 715 9 Use Taylor series to nd the following limits sin a 5 quot I I a liming m b liming Sin

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