Name ID: 1 K L2G0[1O5v MKhustkaO [SnonfKtOwsatrYex ]LwLECF.Y s vagldlq GrWiegOhHtSsN qrzehscexrnvbehdi. -1-

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1 Calculus Name ID: K LG[O5v MKhustkaO [SnonfKtOwsatrYe ]LwLECF.Y s vagldlq GrWiegOhHtSsN qrzehscexrnvbehdi. Assignment For each roblem, find the average value of the function over the given interval. ) f () = ; [-, - ] ) f () = - + ; [, ] Date Period ) f () = - + 5; [, ] ) f () = sec tan ; [-, ] For each roblem, find F ' (). 5) F () = (-t + t - 5) dt ) F () = (t - t - ) dt 7) F () = (t ) dt 8) F () = - (-t + ) dt - t RSSe5\ rkduqt]ah \SVo^fothw`aOrXeV hl_lvcs.e Y naulal^ ]roiigdhutzsf Rr`ebs\ewr[vVeHdz.b a smvacdled MwiiFtth^ EIsnsfiYnXiDtPeZ CGaClhc[usl`u_sG. --

2 For each roblem, find the volume of the solid that results when the region enclosed b the curves is revolved about the the given ais. 9) = - +, = Ais: = ) =, =, = Ais: = Evaluate each definite integral. ) ( + 7) d ) - ( ) d ) - - sin d ) (- + - ) d - 5) ( + ) d - G RXIM5e ikhudtoab PSwo[fetBwaArUeg gl_lnce. v kaulalg `rwi^gthtosu brvehszevrfvdendv.u U fmlamddek EwPimtGhB TIJnFf[iGnqigthen JCfa`l]cwuklUuSsN. --

3 ) - csc cot d 7) ( - - ) d 8) (- - ) d 9) d ) ( - - 5) d For each roblem, find the values of c that satisf the Mean Value Theorem. ) = ; [-, ] ) = + + ; [-, - ] ) = - ; [, ] ) = - + ; [-, ] \ ^beo5z K_uft\aX sskovfmtqwiairter bldldcw.l n fa[lklp criipglhztwsa rpepsleiryvgeodz.e r McaIder ewwiatjhf fimnmfeiinyibtgei UCEaJlhcuuilTuts. --

4 For each roblem, use the method of clindrical shells to find the volume of the solid that results when the region enclosed b the curves is revolved about the the given ais. 5) =, =, = Ais: = - ) =, =, =, = Ais: = 7) = +, = + Ais: = - 8) = - + 5, =, =, = Ais: = For each roblem, find the volume of the secified solid. 9) The base of a solid is the region enclosed b = and =. Cross-sections erendicular to the -ais are isosceles right triangles with the hotenuse in the base. ) The base of a solid is the region enclosed b the semicircle = - and the -ais. Cross-sections erendicular to the -ais are semicircles. B vn`c5f K]untBaY dsjonfmtiwanrde LtLMC[.q E faolfl\ rlirgkhgtxsf [rge]sqesr[vmedi.k CMaaVdweF Yw\inthh` di[nufji`n\ipttes ncoadlfcuzlwuos_. --

5 ) The base of a solid is the region enclosed b the semicircle = 5 - and the -ais. Cross-sections erendicular to the -ais are isosceles right triangles with the hotenuse in the base. ) The base of a solid is the region enclosed b = - + and =. Cross-sections erendicular to the -ais are isosceles right triangles with one leg in the -lane. For each roblem, find the area of the region enclosed b the curves. ) = -, =, = -, = - ) = + +, = = -, = + - 5, 5) = + +, =, = -, = ) = , = + 8 +, = -, = NgFu5Y BKruutBal fsoeflttwianrved BLLLdCR.H t TAYlFlY PrgiXgThtlsb crreusverqveends.v O zmiaidfe\ KwSintkhP ji[n^fqi\ni[txeh [ClaJl`cauhl\ursw. -5-

6 Sketch the sloe field for each differential equation. 7) d d = 8) d d = Find the general solution of each differential equation. 9) d d = + ) d d = e ) d d = e - ) d d = e t h]_m5r KAugtFaH YSSoNfftLwqaGrve `LZLzC`.o V AjlNlR QroiggohEtsC qresneergvhedq.o j NM]aHddeR wlidtfh[ LIXnZfAiInFiHtoeI DCWa^lAczu_l]u[sP. --

7 Calculus Name ID: U hiu[5k qksuht_a[ SJoSfst`wzareX rlnlqc.r c zahll[ NrbiqgHhgtSs] orzescelrxvjehde. Assignment For each roblem, find the average value of the function over the given interval. Date Period ) f () = ; [-, - ] = ) f () = - + ; [, ] -». ) f () = - + 5; [, ]» -. ) f () = sec tan ; [-, ] For each roblem, find F ' (). 5) F () = (-t + t - 5) dt F ' () = ) F () = (t - t - ) dt F ' () = 8-7 7) F () = (t ) dt - F ' () = - 8) F () = (-t + ) dt - F ' () = - + S YYog5C YKCu[taz uscohfjt`wavroeb BLoLZCe.j J nakl_l_ rrjicgohtzsa YrCelsreDrRvgeRdR.B N gmsad]eh wwfitvhj `Iqnvf_iOniiWte\ gckawlnc[ublsucsr. --

8 For each roblem, find the volume of the solid that results when the region enclosed b the curves is revolved about the the given ais. 9) = - +, = Ais: = ) =, =, = Ais: = (( - + ) ) d = 5 5».79 ( ) d = 5».885 Evaluate each definite integral. ) ( + 7) d - 9 ) - ( ) d ) sin d ) (- + - ) d - 9 = ) - ( + ) d - 5 =.5 v zflj5j LKTuKtka] osuohft^watrdeh elxlbcg.u q jaslrlb ArWiEgChctnsw FrNeFsUenrrvqeNdA.^ Q wm_awdzef [w]idtxhu JIKnOfGigndiMtWeB SC_adlcSuWl`uNs]. --

9 ) - csc cot d -» -.9 7) ( - - ) d -».7 8) (- - ) d 9) d 9 =.5 5 =.5 ) ( - - 5) d» -. For each roblem, find the values of c that satisf the Mean Value Theorem. ) = ; [-, ] { } ) = {- } + + ; [-, - ] ) = - ; [, ] { } ) = - { } + ; [-, ] U chl5e FKNuttDa] KStoDfztDwla[rWer elwlvcq.n Z ballplp Crci[gEhgtRsU rrnetsuearkvzeda._ q amqajdbew Twqiotrh\ WIgnYfAiZnDiJtqeH cchawlvcnunlyujsy. --

10 For each roblem, use the method of clindrical shells to find the volume of the solid that results when the region enclosed b the curves is revolved about the the given ais. 5) =, =, = Ais: = - = 5 ( + )( - ) d ) =, =, =, = Ais: = ( - ) d = 7 5 7) = +, = + Ais: = - = 9 ( + )( + - ( + )) d 8) = - + 5, =, =, = Ais: = = 8 (- + 5 ) d For each roblem, find the volume of the secified solid. 9) The base of a solid is the region enclosed b = and =. Cross-sections erendicular to the -ais are isosceles right triangles with the hotenuse in the base. - ( - ) d = 8 5» 8.5 ) The base of a solid is the region enclosed b the semicircle = - and the -ais. Cross-sections erendicular to the -ais are semicircles. 8 - ( - ) d =».97 S Ljuj5T KruStNaA nsfocfttuwfaaroeo LbLdCi.r P EAHlJll rkitgkhhtjsm RrGeOsIeqrUvTe[dh.h o IMbaqdkeT TwXiutlh[ \InafbitnUiHtleF jcvaulvcvuylkuysa. --

11 ) The base of a solid is the region enclosed b the semicircle = 5 - and the -ais. Cross-sections erendicular to the -ais are isosceles right triangles with the hotenuse in the base ( 5 - ) d = 5».7 ) The base of a solid is the region enclosed b = - + and =. Cross-sections erendicular to the -ais are isosceles right triangles with one leg in the -lane. - ( - + ) d = 5 5» 7.7 For each roblem, find the area of the region enclosed b the curves. ) = -, =, = -, = - ( - + ) d - = 5 ) = + +, = = -, = - ( ( =» , )) d 5) = + +, =, = -, = - ( ( )) d =».7 ) = , = + 8 +, = -, = - ( ( )) d = 9 [ KbKa5Y SKru_tSaA ISVoCftqwZaroeD sltl^cv.e V wa_lulo Zr\i[gfh`t`ss PrZeHsqeHrBvoemdN.F \ GMCaBdeV wuiotzha qijnif^imnwimt]ef mcaaalecfuvl_unsr. -5-

12 Sketch the sloe field for each differential equation. 7) d d = 8) d d = Find the general solution of each differential equation. 9) d d = + = C = - + C ) d d = e e = + C = ln ( + C) ) d d = e - e = e + C = ln ( e + C) ) d d = e -e - = + C = - ln ( - ) + C Q AF\5[ PKRuKtqab rseovf]tfwbazrsev clslkct.\ [ A[lKlf ^rkiqglhotcsi vrvemsyebrvvoebde.t K ^MkaudMeA Gw_iNtrhF DIenLfvin^iatWej ]CablScgu_lUursh. --