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Quiz1_Solns - Name idlUHOH Date MACZ312_FalI2011_Siegel...

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Unformatted text preview: Name: idlUHOH§ Date: MACZ312_FalI2011_Siegel Quiz #1 Score: / 31 Directions: Show all work for full credit. Write all answers in the blanks provided if possible. 1) (4 pts. ) Verify that sinh(2x)— — 23inhxcoshx. H(int: You may work both sides separately and see if you can find the ) K_ ewx my 5 I HMS; gxxpreessmn 2K 52 $th (fish X “SQ/emf) 2/657“ Xi» 6 :g’ZKpg/o 776/0:___£/C9n__ 6 fiZX :(e 2Xm_€-- ”ZX' 50 LIV/S /7/—/$ 2%? Wong/5W3 ~-—~ 2. MT , 2) (5 pts.) lfy— — —31n [sech(5x — 2x3)], find y’. Simplify completely. Answer: y’ = §[5'6X 2) fad/7h (Phi/ta L M / pm) Mmh (fix-aw) (3%) XXX] sea ._ X e a (‘5 ~exz) ffl%/M[5 x 2x 3) 3) (6 pts.) Find the indefinite integral fidx. sinh2 (16x—3x2) Answer: (3 ”If; ([)’[”h (MD/Yigx'a +6? “SIQXPZIX'Z” “r ‘5’” 3X d“ eggs/é} em SIM/7%) Zzw-ex pix/f. ”(l/x MX doe—«~9— 'L cg}; 2(a) cit/L 56%” ” 5/7M26u) 516M): \ : é, [mmzfé (a) )+C [email protected]@ ft: N 4) Find the area between f(x) = 5x3 + x2 and g(x) = x2 + 45x by doing the following: a) (2 pts.) Find all values of x where f and g intersect. "’32 Oz 3 Y'FV. I. flaw) O EXZM/{i‘flqu 576:6) 0V X'Z‘wqfo 57-9-4bxrd ‘ X'rd9 or X236} i . _,v-=I~ ihferéccfibn Pb: X” 0 a r X ” fl 3 b) (2 pts.) Between each intempt, test a value in each interval in fand g to see which is on top. i {'DW/LOF jam/opt ><f Xe»; .XH (X K '1'“ '\ 2:.wa c) (5 pts.) Find the area between fand 9. Area: Wflfi/ firf affirm ”3 (xflctx “”fgiflo‘” [1m] olx. .: J “235%,; X2) --(x 25451de 5/14“ 56/51) —{5‘2r 35x9] 50-) 0 Z, ‘/ eff/‘5 ”5/005 +f (55x~—57<3)alx: .él" 42‘." 13+ 43* {I 7/3 :[cm— {—580 %5(9))J+[ [@MWM-é; 75/))—(0)j] ‘ : [.— (1505“. $05)] [5051??? [’_ (3:7 55:40) ]7‘" 8;}? 4:; 4052/.) @105; 42054105“ 6...? 202,5 :@ {Jazz‘s Z 5) Find the volume of the solid formed by revolving the region bounded by y— — —x3, y= 4, and x= 0 about the line y= 6. Use the Disk Method for this problem. (w warmer Method ) a) (2 pts.) Draw a graph of the region to be revolved. Include the representative rectangle on your graph. [5 ~ 5% 3/553) = 35 ~532< '35 3x 55M 69 (5 (pts ) Find the volume of the revolved region. Volume:____ szé_éxz)z ,(2>]0I)< rf[ [25 pm arfixé) ~4/] 5M ”f @zwghlx‘fldx ~77 [22x @354 {1597M 7‘ [52(2) "31455 4—25/ 4((7/5L7 :17[[04,Zq+ 2$J 1‘ V1405??? J 77' [2323 :5ch ...
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