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# Review Sheet for MATH 1432 at UH

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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 Houston taught by a professor in Fall. Since its upload, it has received 19 views.

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Date Created: 02/06/15
Department of Mathematics University of Houston Math 1432 David Blecher Some review questions for the Final Note that there is some duplication of questions below For example7 on the real nal you d have one of questions 8 and 97 not both7 and similarly for some of the other questions 1 Let gz 5x3 7 4x2 7 2 Find an equation for the normal line to the graph ofg 1 at the point 727 0 to 1 Find h z if Mm for m gt 0 ii Find limmace mm and limmno mm iii What is lime 1 gm iv What is limmao 3 Differentiate each of the following functions a sec 1z3 b lncoshz c log41 2m d 7 l 4 Find the following integrals a m dz b 01 tan lm dz c 521 cosm dn cm 1 d ltegt d f 1 2 d 4n2 4 7 352W2 0 x6 1 1 53 5 Find the following integral 2 dz 1 m m 7 6 5 13 6 1 xx71 7 In each of the following write down if the series converges or diverges7 giving reasons dz Does this converge To what a 7 b 7 c k4 7k47l HEW1 HEM g 00 M t 71 kink d 2 E e 221 6 221 k1 8 Note that on the real nal you d probably only have to do a and b below 00 k a Find the interval of convergence of Z W Justify k0 b Find the integrated power series of the series in a c Show that the sum of the series in b is 22772 k 1M d Set x Z T for z in the interval of convergence from a Show by differentiating k0 the expression in c7 that x for x in the interval of convergence d Setting an 1 in d nd 221 3 9 Note that on the real nal you d probably only have to do a and b below a or w at va ues o z oes t e series 7k converge or t ese va ues o z w at is t e sum F h l f d h 2 0 3k F h l f h h of the series b Consider the series 210 What is its radius of convergence c What is the sum of the series in b7 if 71 lt z lt 1 Hint integrate the expressions in a d What is 2200 m Hint choose z carefully in 1 10 11 12 13 14 Find the Taylor series for x 1n2 7 Write down the rst four terms out in full Using the Lagrange formula7 nd a Taylor series approximation for sin1 with error lt 0001 Give an equation of the tangent line to the curve given parametrically as Mt sin 57 yt cost at the point 01 Sketch the polar curve r 17 cos 0 for 0 g 9 g 27139 Find the length of the curve in question 13

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