MATH 1080: Calculus of One Variable II Spring 2018 Textbook: Single Variable Calculus: Early Transcendentals, 7e, by James Stewart.

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1 MATH 1080: Clulus of One Vrile II Spring 2018 Textook: Single Vrile Clulus: Erly Trnsenentls, 7e, y Jmes Stewrt Unit 2 Skill Set Importnt: Stuents shoul expet test questions tht require synthesis of these skills. Aitionlly, some test questions my require synthesis of mteril lerne in the urrent unit n previous units. Note: Tehnology is not llowe on ny exms. Limits of integrtion for efinite integrls shoul e written s ext vlues. The vlues for efinite integrls shoul lso e written s ext vlues. Setion 7.3: Trigonometri Sustitution, pp WeAssign: 5, 7, 9, 11, 23, 27, 29, 37 We o not over hyperoli sustitutions. Evlute n integrl using the given sustitution. Drw the ssoite right tringle. Use trigonometri sustitutions to evlute integrls , 5, 7, 9, 12, 13, 15, 29, 30 Complete the squre n then use trigonometri sustitution to evlute the integrl. 23, 24, 27 Explortion. 31 Applitions involving integrtion using trigonometri sustitution. 33, 34, 37, 38

2 Setion 7.4: Integrtion of Rtionl Funtions y Prtil Frtions, pp WeAssign: 3, 12, 15, 19, 23, 29, 33, 35, 39 Write out the form of the prtil frtion eomposition. 1 6 Expn n integrn y prtil frtions n evlute the integrl. 9, 12, 19, 25, 26, 30, 31, 34, 35 Use long ivision n then prtil frtion eomposition if neessry to evlute n integrl. 7, 8, 15, 16, 21 Use sustitution to express n integrn s rtionl funtion n then evlute the integrl using prtil frtion 39, 45, 47, 48 eomposition. Explortion. 56 Applitions involving integrtion n prtil frtion eomposition , 72 Setion 7.5: Strtegy for Integrtion, pp WeAssign: 1, 5, 7, 9, 15, 19, 25, 27, 37, 41, 49, 63 Evlute the integrls 1 82 Explortion. 83, 84 Review Setion 4.4: Ineterminte Forms n L Hospitl s Rule, pp Determine the form of the limit. 1 6 Ineterminte Forms: 0 n 9, 12 16, 20, 22, 31, 32, 0 35, 38 Ineterminte Forms: 0 n 40, 46, 47, 49, 50, 54 Ineterminte Powers: 1, 0 0, n , 60, 62 Explortion 73, 74

3 Setion 7.8: Improper Integrls, pp WeAssign: 1, 7, 9, 13, 15, 23, 27, 31, 33, 35, 49, 51, 55 Ientify improper integrls of Type I ( f(x)x). Ientify improper integrls of Type II f(x) x or ( f(x) x), where there is isontinuity t some point,, or where < < ). Determine whether n integrl is onvergent or ivergent. Evlute onvergent integrls. Use the Comprison Theorem to etermine whether the integrl is onvergent or ivergent. Use n improper integrl to fin n re or volume (if the re or volume is finite) n other pplitions. Fin vlues of p for whih n integrl onverges. (Exmple 4, p. 522) 1, 2 7, 10, 15, 16, 18, 21, 23, 26, 34 36, 40 49, 50 3, 44, 45, 63, 71, 75,76 57 Chpter 7 Review Prolems, pp Exerises 1 50, Setion 8.1: Ar Length, pp WeAssign: 7, 11, 13, 17, 31, 33 Use the Ar Length formul L = 1 + [f (x)] 2 fin the length of the urve y = f(x), x, given f (x) is ontinuous on [, ]. Or for x = g(y), y, given g (y) is ontinuous on [, ], L = 1 + [g (y)] 2 x x to Use the Ar Length Funtion, s(x) = 1 + [f (t)] 2 t. x 1, 2, 10, 13 15, 17, , 35 Aitionl Conepts 31, 32, 35 Applitions of Ar Length 29, 33

4 Setion 8.2: Are of Surfe of Revolution, pp WeAssign: 7, 11, 13, 15, 25 Use the formul for the surfe re of the soli otine y rotting the urve out the x-xis: y = f(x), x, given f (x) is ontinuous on [, ], S = 2πf(x) 1 + [f (x)] 2 x = 2πy 1 + [ y 2 x ] x. If the urve is esrie s x = g(y), y, use formul efine in terms of y for the surfe re of the soli otine y rotting the urve out the x-xis: S = 2πy 1 + [ x 2 y ] y. Use the formul for the surfe re of the soli otine y rotting the urve out the y-xis: y = f(x), x, given f (x) is ontinuous on [, ], S = 2πx 1 + [ y 2 x ] x. If the urve is esrie s x = g(y), y, use formul efine in terms of y for the surfe re of the soli otine y rotting the urve out the y-xis: S = 2πg(y) 1 + [ x 2 y ] y. 8, 9 6, Applition of Surfe Are 25, 28, 31, 33

5 Chpter 8 Review Prolems, pp Exerises Prolems from the Text Conepts: 1, 2 Exerises: 1-4, 7, 8 Setion 11.1: Sequenes, pp WeAssign: 1, 5, 11, 15, 21, 25, 27, 29, 31, 33, 35, 41, 43, 45, 47, 49, 73, 75 Conepts 1, 2, 71 List terms of sequene. Fin formul for the generl term of sequene o, Determine whether sequene is onvergent or ivergent. If sequene is onvergent, fin the limit. Determine whether sequene is inresing, eresing, or not monotoni. Determine if sequene is oune , 76, 78 Setion 11.2: Series, pp WeAssign: 1, 3, 5, 15, 19, 23, 27, 31, 35, 43, 47, 53 Define n infinite series. Explin wht it mens for n infinite series (versus sequene) to e onvergent or ivergent. Interpret infinite series nottion. Explin the reltionship of series to its sequene of prtil sums. Determine whether geometri series is onvergent or ivergent. If it is onvergent, then its sum is r n 1 n=1 = 1 1 r, r < 1. If r 1, the geometri series is ivergent. Determine whether series is onvergent or ivergent. If it onverges, fin its sum. Express the series s telesoping series n etermine if it onverges or iverges y using the efinition of series (pp. 705). Express numer s rtio of integers. 1, 2, 15, o, o o