Math 172 Fall 2019 Exam 1a answers - Math 172 Fall 2019 Exam 1 Problem 1 2 3 4 5 6 Total Worth 15 20 20 10 21 14 100 Sorry about the handwriting I'm

Math 172 Fall 2019 Exam 1a answers - Math 172 Fall 2019...

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Math 172 Fall 2019 Exam 1 Problem 1 2 3 4 5 6 Total Worth 15 20 20 10 21 14 100 Possibly Useful Trig Facts: sin ቀ ቁ ൌ √2 /2 cos ቀ ቁ ൌ √2 /2 sin 2 ሺ࠵?ሻ ൅ cos 2 ሺ࠵?ሻ ൌ 1 tan 2 ሺ࠵?ሻ ൅ 1 ൌ sec 2 ሺ࠵?ሻ sin 2 ሺ࠵?ሻ ൌ 1 2 ሺ1 െ cosሺ2࠵?ሻሻ , cos 2 ሺ࠵?ሻ ൌ 1 2 ሺ1 ൅ cos 2 ሺ࠵?ሻሻ Remember to show all of your work and provide all necessary explanations for full credit. Good luck! Sorry about the messy handwriting I'm practicing with my tablet
Problem 1. (a)(5 points) Sketch the region between the graphs of . (b)(10 points) Find the area of the region from part (a).
Problem 2. (20 points) Let ࠵?be the region bounded by the following curves: ࠵? ൌ࠵?, ࠵? ൌ 2and ࠵? ൌ 0. Use the washermethodto find the volume of the solid generated when ࠵?is revolved about the ࠵?-axis. outerradioszBInnerradius7142lDrfo4tECx77dxiTSo4XdxtL4xHoEx48t160EGGof
Problem 3. (20 points) Let ࠵?be the region bounded by the following curves: ࠵? ൌ࠵?, ࠵? ൌ 2and ࠵? ൌ 0. Use the method of cylindrical shellsto find the volume of the solid generated when ࠵?is revolved about the ࠵?-axis. Note that this is the same solid as considered by problem 2. DyV5o2ttYXdy2xaxis2ty.ydy Y_X Xzity4To168Mostequalanswertoproblem 2
Problem 4. (10 points) Write an integral representing the arc length of the graph of ࠵? ൌ √3࠵?on the interval [1,2ሿ. DO NOT EVALUATE. 2dxBtx'tJabFtdxIFE Fs
Problem 5. Evaluate the following expressions (7 points each) (a)ௗ௫ln | secሺ࠵?ሻ |(b)∫ 5࠵?࠵?(c)ୡ୭ୱ ሺ୶ሻୱ୧୬ ሺ௫ሻగ/2గ/ସ࠵?࠵?seemSecktankss.ecseccxytanlxIsxeensxSexhMdxLncgexlncsTex'hasbIn5usinkIutdulnlu.LKdusixdyfluidenftzXutzffor.ggEnlilCenabeliefxEuize
Problem 6. Evaluate the following expressions (7 points each) (a)ௗ௫sinh2ሺ࠵?ሻ(b)ୡ୭ୱ୦ ሺ௫ሻ௘+ୱ୧୬୦ ሺ௫ሻ࠵?࠵?t2sin.baScosh5fedulnI4ltCuetsinhNlnetsinhlxYtCJducosh4DX

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