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# Calculus II MAC 2312

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This 3 page Class Notes was uploaded by Mozell Veum on Monday October 12, 2015. The Class Notes belongs to MAC 2312 at Florida International University taught by Steven Hudson in Fall. Since its upload, it has received 13 views. For similar materials see /class/221705/mac-2312-florida-international-university in Calculus and Pre Calculus at Florida International University.

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Date Created: 10/12/15

MAC 2312 April 2003 Review Sheet Prof S Hudson The final exam will be Thursday April 24 930 to 1215pm It will cover the entire course About half covers topics after Exam 3 HW6 and 7 Chs 9 and 10 Remember that no incompletes will be given except for emergencies Settle any un nished business such as late HW with me by Tuesday 41503 But if you have questions about calculus you are welcome to ask anytime I would suggest email but expect to be in on TR afternoons up to 424 A Suggested Review 1 Look over all the HW problems from Chs 9 and 10 until you are sure you can handle any similar problems Include the Ch 93 and 94 problems which are not to hand in Note pages 769 770 especially problems 16 44 2 Memorize the Taylor series highlighted in the text including page 704 1 pages 711 714 19 21 22 27 page 746 14 and page 748 19 This is easier if you focus on patterns and similarities From this base you should be able to quickly find the series for examples like fac sin2x etc 3 Know and be able to use Taylor7s formula for Rnx as done in class For showing convergence see Examples 5 6 on page 710 I cannot find any HW exercises in the text like these For error estimation see Example 7 on page 757 you may need a calculator but not a graphing one See exercises 29 40 in Ch 109 Think about when to use R7 or the ASthm or p the Ratio Test 4 A rough guide to Ch 9 omit 91 know the highlighted formulas in 92 3 know which formulas go with roses cardioids etc and know the parts of 94 covered in class on 41503 expect some announcement in class Practice problems like 25 36 in Ch 93 5 Main proofs and explanations to know Page 352 eqn 7 FTC Part I Page 411 eqn 5 Disk method Page 707 eqn 7 the formula for the Taylor coeff7s Page 640 eqn 1 polar area formula 6 Earlier topics Review Chs 5 7 and HWs 1 5 as needed l7d expect about a day or so of this should be enough Check that you haven7t forgotten any major definitions eg the integral average value or formulas shells lnexp Simpson7s rule or methods trig integrals partial fractions etc B Here are some sample problems that you can use for more practice Some are relatively hard problems from old exams There are more old exams on my web site 1 Compute or show that it diverges fooo sinac die 2 Compute f f M dac ftan 12x dac fsin2ac cos3x die The volume y 12 2 and y at over at E 0 2 revolved around the x axis 3 Use the usual series for cosx to approximate cosl to four decimal place accuracy to within 00005 You can leave your answer as a sum don7t simplify it Use the Rn formula to find the smallest allowable n Hintsz 6l720 7l5040 8l40320 9l362880 4 Answer True or False The formula for the trapezoidal rule is ZETGMJO 2241 22474 yn The formula for arc length is L fab 27raml fac2 dx When we eliminate the parameter from the equations x 2t 7 3 and y 6t 7 l we get that y is a linear function of x Theseries l7ll7l171convergest00 The McLaurin series for sinac is l 7 332 44l and it converges for all real x lf 2 ak converges absolutely then 27ak converges absolutely too Every monotone sequence that is bounded above converges at ln2 has a McLaurin series The graph of 7 cos46 is a 4 petal rose 5 Sketch the curves and find formulas for the area You don7t have to compute the integrals A The region inside the curve 7 l cos 6 B The region inside the curve 7 4 4 cos l but outside of 7 6 C The region enclosed by the inner loop of the curve 7 l 2 cos 6 6 Use the left endpoint rule With n 4 to approximate the area described in 5A 7 How much work to pump the water over the top of the reservoir It is cone shaped With a 20 foot diameter at the top and is 15 feet deep It is filled With water 62 lbs per cubic ft to a depth of 10 feet

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