DIFFEREN AND INTEGRAL CALCULUS
DIFFEREN AND INTEGRAL CALCULUS M 408C
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This 5 page Study Guide was uploaded by Reyes Glover on Sunday September 6, 2015. The Study Guide belongs to M 408C at University of Texas at Austin taught by Staff in Fall. Since its upload, it has received 44 views. For similar materials see /class/181489/m-408c-university-of-texas-at-austin in Mathematics (M) at University of Texas at Austin.
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Date Created: 09/06/15
UT Learning Center 5 urwvc 39 Succeed r Excel lt M4080 Final Exam Review Day 2 Related Rates 1 Two boats are mcing with constant speed toward a nish marker boat A sailing from the south at 13 mph and boat B approaching from the east When equidistant from the marker the boats are 16 miles apart and the distance between them is decreasing at the rate of 17 mph Which boat will win the race 2 Ifa snowball melts so that its surface area decreases at arate of1 cmZmin nd the mte at which the diameter decreases when the diameter is 24 cm 3 A balloon rises at the rate of 10 feet per second from a point ofthe ground 100 feet from an observer Find the rate of change of the angle of elevation of the balloon from the observer when the balloon is 100 feet above the ground Linear Approximations and Differentials Z 4 A Use differentials to approximate 8063 B Use differentials to estimate the amount of foam needed to apply a layer 1 cm thick across the surface of a hemispherical dome with a diameter of 20 m Volume of a sphere is given by V 727 Optimization Problems 5 Find the points on the parabolay 4x2 1 closest to the point 06 Hint distance formula is d 406 Xe 2 y yo 2 6 A right circular cylinder with a bottom and a top is to be designed to hold 12 uid ounces of a soft drink and to use a minimum of material in its construction Find the required dimensions for the container 1 oz 5 18 in3 7 A power line is needed to connect a power station on the shore of a river to an island 4 kilometers downstream and l kilometer offshore Find the minimum cost for such a line given that is costs 50000 per kilometer to lay wire under water and 30000 per kilometer to lay wire under ground Island Power Station I I nZ 2M3 0 1 m3 712V 2 12 2 3M4 m4 WELEM viL z V277 xz 7B212 372 12 A a I A I A a I 127 x2 7 60 oan 40 KY 10 7n6 11m W 51417 V3 51737 7 2 712 z 712 7 2 5n4 7n4 az2bzc0 7 zwl 7 27 2 Vi27 2 2a 4M3 3mg 5M3 7127 62 01 127 V372 xcos 6 ysin9 l39 39 71 limfglin1flimg limfglin1flimg hm l1n1M 1 limM 0 g 11mg 170 az 0270 az sinzl cosz cos zl 7sinz tanzl se02z seczl secztanz csc zl 7csczcotz cot zl 70502z 7 f Qfifg dy dydu CY 70 W 7W 1 w 7 f yfy E 7 T y fltugtu7gltzgt 7 a 7 g m fa f az 7 a When z m d Af m f aAz When Az m 0 Linear approx Rolle s Thm If u then fc 0 for some 5 6 ab Mean Value Thm w fc for some 5 6 ab a 1 7 m b fltzgt dz 7 F02 7 Fltagt Abfzdz7bafz dz f9ry r d1 u duv u 91 g f N dtl 7 m Abfltzgtdz7ffltzgtdzffltzgtdz afr yz dz afrdz 9I deal I m fz M mb7a fzdz Mb7al b gun 7gltagt 7 was dead udvuv7vdul AreaQ f hz 7 gz dzl VolS f N 7 wg2z dz solid of revolution VolS f Az dz general solid lnab lna lnb ab eaeb lne z sinarcsin z z lnab lna 7 lnb ea7b eaeb emy y arcsinsin t9 9 e0 7 lncp plnc lne 1 ln1 0 el e 60 1 log z lnzln 751quot e i 2718 tanarctan z z arctantan t9 t9 arcsin zl fexdze C dz arcsinz C 1 fm 7 M lln91l Mm 691 690091 arcsingz fidzlnlzlC f a 17 dz arcsin C lnle 7 i l xl 1M 5 arctan zl H7105 f5 d9 13 f H7105 dz arctanz C 0 In lyrll 7 31 WV 7 one WW arctangz 272 f 32 dz iarctan C sinhz 26771 coshz 617 tanhz iTrg cschz sechz 81M cothz m sinh my coshz cosh my sinhz tanh my sech2 z csch my 7 cschz cothz sech my 7 sechz tanhz Goth my 7 CSCh2 z tan9sint9Cost9 cott9cost9sint9 560910059 05091sin9 cott91tant9 sin2 9 0052 9 1 1 tan2 9 sec2 9 1 0012 9 CSC2 9 sin2 9 7 00529 0052 9 COS26 sint cost sineg singcos 45 sint9 7 sint9 sinO sinqb cos6 7 15 7 0059 15 Cos Bees 15 cos9 7 lt15 cos6 15 sinA i B sinA cosB i cosA sinB cosA i B cosA cosB I sinA sinB fsinzdz7coszC fooszdzsinzC ftanzdzln secz C fosczdzln cscz7cotz c fseczdzln secztanz c footzdzln sinz C P 7 2 2 P7 AzB D E1 E2 degPltdegQ7 Q7az bzczdze gt 67 a12bxcrdre7ze2
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