MATH 1080: Calculus of One Variable II Fall 2017 Textbook: Single Variable Calculus: Early Transcendentals, 7e, by James Stewart.

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1 MATH 1080: Clculus of One Vrile II Fll 2017 Textook: Single Vrile Clculus: Erly Trnscendentls, 7e, y Jmes Stewrt Unit 2 Skill Set Importnt: Students should expect test questions tht require synthesis of these skills. Additionlly, some test questions my require synthesis of mteril lerned in the current unit nd previous units. Note: Technology is not llowed on ny exms. Limits of integrtion for definite integrls should e written s exct vlues. The vlues for definite integrls should lso e written s exct vlues. Section 7.4: Integrtion of Rtionl Functions y Prtil Frctions, pp WeAssign: 3, 12, 15, 19, 23, 29, 33, 35, 39 Write out the form of the prtil frction decomposition. 1 6 Expnd n integrnd y prtil frctions nd evlute the integrl. 9, 12, 19, 25, 26, 30, 31, 34, 35 Use long division nd then prtil frction decomposition if necessry to evlute n integrl. 7, 8, 15, 16, 21 Use sustitution to express n integrnd s rtionl function nd then evlute the integrl using prtil frction 39, 45, 47, 48 decomposition. Explortion. 56 Applictions involving integrtion nd prtil frction decomposition , 72 Section 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

2 Review Section 4.4: Indeterminte Forms nd L Hospitl s Rule, pp Determine the form of the limit. 1 6 Indeterminte Forms: 0 nd 9, 12 16, 20, 22, 31, 32, 0 35, 38 Indeterminte Forms: 0 nd 40, 46, 47, 49, 50, 54 Indeterminte Powers: 1, 0 0, nd , 60, 62 Explortion 73, 74 Section 7.8: Improper Integrls, pp WeAssign: 1, 7, 9, 13, 15, 23, 27, 31, 33, 35, 49, 51, 55 Identify improper integrls of Type I ( f(x)dx). Identify improper integrls of Type II f(x) dx or ( f(x) dx), where there is discontinuity t some point,, or c where < c < ). Determine whether n integrl is convergent or divergent. Evlute convergent integrls. Use the Comprison Theorem to determine whether the integrl is convergent or divergent. Use n improper integrl to find n re or volume (if the re or volume is finite) nd other pplictions. Find vlues of p for which n integrl converges. (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 Exercises 1 50, 72 76

3 Section 8.1: Arc Length, pp WeAssign: 7, 11, 13, 17, 31, 33 Use the Arc Length formul L = 1 + [f (x)] 2 find the length of the curve y = f(x), x, given f (x) is continuous on [, ]. Or for x = g(y), c y d, given g (y) is continuous on [c, d], L = 1 + [g (y)] 2 dx c d dx to Use the Arc Length Function, s(x) = 1 + [f (t)] 2 dt. x 1, 2, 10, 13 15, 17, , 35 Additionl Concepts 31, 32, 35 Applictions of Arc Length 29, 33

4 Section 8.2: Are of Surfce of Revolution, pp WeAssign: 7, 11, 13, 15, 25 Use the formul for the surfce re of the solid otined y rotting the curve out the x-xis: y = f(x), x, given f (x) is continuous on [, ], S = 2πf(x) 1 + [f (x)] 2 dx = 2πy 1 + [ dy 2 dx ] dx. If the curve is descried s x = g(y), c y d, use formul defined in terms of y for the surfce re of the solid otined y rotting the curve out the x-xis: d S = 2πy 1 + [ dx 2 dy ] dy. c Use the formul for the surfce re of the solid otined y rotting the curve out the y-xis: y = f(x), x, given f (x) is continuous on [, ], S = 2πx 1 + [ dy 2 dx ] dx. If the curve is descried s x = g(y), c y d, use formul defined in terms of y for the surfce re of the solid otined y rotting the curve out the y-xis: d S = 2πg(y) 1 + [ dx 2 dy ] dy. c 8, 9 6, Appliction of Surfce Are 25, 28, 31, 33

5 Chpter 8 Review Prolems, pp Exercises Prolems from the Text Concepts: 1, 2 Exercises: 1-4, 7, 8 Section 11.1: Sequences, pp WeAssign: 1, 5, 11, 15, 21, 25, 27, 29, 31, 33, 35, 41, 43, 45, 47, 49, 73, 75 Concepts 1, 2, 71 List terms of sequence. Find formul for the generl term of sequence odd, Determine whether sequence is convergent or divergent. If sequence is convergent, find the limit. Determine whether sequence is incresing, decresing, or not monotonic. Determine if sequence is ounded , 76, 78 Section 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 sequence) to e convergent or divergent. Interpret infinite series nottion. Explin the reltionship of series to its sequence of prtil sums. Determine whether geometric series is convergent or divergent. If it is convergent, then its sum is r n 1 n=1 = 1 1 r, r < 1. If r 1, the geometric series is divergent. Determine whether series is convergent or divergent. If it converges, find its sum. Express the series s telescoping series nd determine if it converges or diverges y using the definition of series (pp. 705). Express numer s rtio of integers. 1, 2, 15, odd, odd odd

6 Section 11.3: The Integrl Test nd Estimtes of Sums, pp WeAssign: 5, 7, 11, 15, 23, 25, 27, 29, 37, 39 Prolems from the Text Concepts 1, 2, 27, 28 Use the Integrl Test. n is convergent if nd only if f(x) dx is convergent, n=1 1 given tht f is continuous, positive, decresing function on [1, ) nd n = f(n). 3 8 Determine if the series is convergent or divergent odd Find the vlues of p for which the series is convergent. 29, 31 Find the sum of series. 35, 36 Estimtes of sums using the Reminder Estimte for the Integrl Test Section 11.4: The Comprison Tests, pp WeAssign: 1, 2, 3, 5, 13, 15, 17, 23, 25, 31 Note: For some prolems in this section, either the Comprison Test or the Limit Comprison Test will work. And for some prolems previous test will lso work. We do not cover estimting sums in this section. Concepts 1, 2 Use the Comprison Test. Given two series n nd n with positive terms, If n is convergent nd n n for ll n, then n is lso convergent. If n is divergent nd n n for ll n, then n is lso divergent. Use the Limit Comprison Test. Given series n nd n with positive terms, If lim n = c, where c is finite numer, c > 0, then n n either oth series converge or oth series diverge. 9, 10, 13, odd, 11, 12, 14 20, odd

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

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