__e______&___ _______0_____________00____0________M*w0 _mm______________________0_____,_t__)_mm___________q_n______________t______,_____t__0_t_____p_(________J_y__J_t_____m______q__v________________t____0___________J____________n____n___t____l______Ml__,___t____l___t_t__r_________(_n__(___t_______0_______t___m_t__t_tlvJ_(______pn_p_t_0__________t__t_t____t______________________________t0__r_0____t____________w____________0______p_____h__0_mmh__t_0________t____________________r___t________,__________o__p__0_t_________________0______________ ____,m___________ _myt_tl_________l0t_____________0d_0____t,_______r_____________,______t___ _____ _____0_og________,__0________0____ __ ____(t____)_________0_p0__00_(_____ ___________l_______,0o____0____________________,_____o__________,_,___________)___0__0_________________0________(_________0_,______ _ )Jf

MATM 1 372 _ock _idte_ 21. At _bat pa__ t does _e l_' e wbicb �s _e _apb of _e v_tor _nc_on �(_) -_ __3_ + 20) _+ (7t _ 47) _i_tersect the line which is the graph of the vector functîon �(s) -_ (as + 14) _+ ( _s _ 8) ___ D _ _.._____ _,,,._.,,,.,,d. .,,... ,,,,,Dp,_.,__=,,., _,_,,,_.,...__,_ .,._,,_ ''_.'__'______,,, __d__.'____'_,.d_,.___=, ..._,,,._.'_'__,,,,,,,,, _'' _.,'=',. _ , , _ _ _ , __ ' ' , , w _ =

o,, , _,., 0 _ _ '.;,,, _, - _. .. ', _ ',. _ ,, _ , '. _ ' ,. _ _ o , ,_ , _.A , - ,.. _,, _ = '. _ _ _ _ '. _ ,.., _' _ _; ,.. _ ' _, , , , _. _ _ _ _ ,,,,..,, ,. .0,v_ q , __. ' ' ,. , _ ' _ , ,, .,, ,o , .,,, ,_ , , _. ,. ,,, = _ , _ _,.. , '.. _ _ _ __, _ _ _,q _ S _, _, _ _ __ _ _'^'__ '' '' _,-_J _'_' ,__' ',___-'&Q _._o'_ _'''_'___•__.__ '''___'___,.''''_='._'':,'.;',,,,_'^'"'_,_,, ________ ''- ___a_ ''' '__'' __, 9 __ _ '^'' "''__ _ __' _,., ____''_,, __;,,_ _,..""_'_ _''_'=.__,=,',,.._'_';',._'' _'__e0'o'y__,0.='=___!,._',.;p, ___ _ _'_'' '"'__=:.,,, ..____ __''__,_',== _0',.__.,;, _'_._ __,, , )_ _ ,..,.,' ' __ ' _'' _''''' ''''' '_ "'' ''4_... _ ._'_ '' _., __ ,, ,_ _ _ ___'__ ,,_ __' '., ,,., , _._'' _' ' ,0_,''' . ,, _,o,'e=_':__, _'''', ''!_',' 0 _ ', ', __ _ _ ', _,,,d _ '' '_ '_ __ t ' _ _ '' __ ' ' ' _ ' _ ' ' ,,._ ' ' _' ' ' ,_ ' ' w ' ' ' ' ' ' ' _ ' _ ' '

2. Considef _e c_e wh�ch �s _e graph of the vect,r €,nct;on _, _ __ 2f3 _ 2_2 + 3 ?; + 4t2 _ Jt + 3 __Find _e vector _nc_on R(_) _hose _aph is _e _angenf line to this c_e at the point on the cu_e wheret __ _._,,, .,0__.._ ' _ ,'' ., ',__, __,,,,'_''___ .,,,. ,,_,, ._'____,,,,. __,. _ (" _ _ _ '_'',,,___'__'__,,__ _ _ _ l .'' _! '' ..0_'',''__,,.,.___.,,, _ __..__,..,,,,___'"''____,_',,..,,_,,.,,,.,,,._,,,.,,_?...,,,,,_•,.,o,.n,, __.,_,,__='_., __'_'',,',.,_,__,_'' .,.__,__ _' _ .\ _' '''_''''','',o _ ,_, ,.="_'''

\ '',.,. __, _o.;,.= o..=,,_,,..., _,_.,.:',__'_ *.. . ,, ., .,,. __, , , &_ _ _

_, ,_ _ ,, _ _ , _, , 0 ' _ __ , ,.. _,d,.. .,.; _' _ ' ' _ ___ ,,, _, , _,,,, ,.,,. ,, ' ' , ,, _, __ ,, , _ ' , _ _ _, ,,.. _.! _ ' ' o _,_ 0 , , - =,, _ _.d.... _.,., ,, _ _ ..,,, _,,, ,,,, _, , , , , _ ,, , ' ' _ ,.,. .., _,.. _. , ,, _ _ 0 _ a , ,r _' _, __ __,m, _,_ _, _,"a'___ _,,,'_' _'''"'''^" _''__"' ____'____ _' _'' '_,.

_ __''_''_,' _,_''_,,,'__.__,,_' _____ _, ___' ,,'_'__, ___ _:,!_q' __ ''''_'" ;

,.. __, __, , _ __,,_,,,,,, _,,_., __,.' ' __'=. _, _, _ ' = =_ _ _.,._,,.,,.,____ _,. _ = _ ',, =,, _',. ___' ''''..''';''..,, _ _ ' = _ ' !__,_ _'"_,.,,_ _ __' ' L ' ' ''9,_ __ '' e ' ' '. ; ;,.,,._, _ _, _ _. '..,_._. _.

___________________/______0___l_______0___my_p%_,_b______y__t________________,_______0,________0_%yp__t________ ______________t_p______0_________________0__l_____0t0_______p_______________t_______t____,__________M_p_t____t_,t____________________________0_________ot____,_______________________0x__0_0______t______0___rp_____r0_______0___________________________________t___________Mp_Mr____t_n_______n_g___n______N__t_____\t__t____________tn___t_0_____'____________o_______________________________________o___________0'________0_____c______,_______00___0___0_________________p_____________0__t_______p___________________0___o___t0________________,__n___0_0_____0_______t0______0__0____0_____o_______________t________________0N_0______0______0t___N_________,__0__________'____yo_,_________________o___0________,'___o__0__________t___________'__________r____________t________________r____r___0___0___________t______r0________t____+___t_t_0__n__t________t__t__r______t__t_____________v_t______r__t_______r___r_____t__m______M__nt_wyn________ym__r__0___&___0____n____|___'___t___ty_____r_____rt____v_____________t_p_tt_t____4_______t___*______t_______t__4r___p__r_t______________________/_____t_____p_________________________r__r_t___________t___t0Dtttm_________tl_h___l_____tt__t\__4____0__s__,__?_____x_______________________________p0__________,____________________________________,______p_0_0__________>w44_________0______0___00_r__\___\_______\_______tt__\__7tmr__J_________f__l___00_____v__0_____________________g0_____,__r)_0t_____t,_0_____/____________,______________________r__'m_'_____J_____t_t_tl__r___r___________________r_________0_________________________h____________________0__________0____o___f_______ _____ __)_? _

__ 1 372 _oc_ Mîdte_ 2

3. Given _e p0int in _e pl_e _i_ rectangul_ coordinates ( _ 3, _ 3 _) , _nd the four d__r_nt setsof polaf coordina_es for this po__. _, ____, ,,w,,,, ,,,, , ,,,, __%_____%_N___ ''__"___~'_'Y'K"'_d_-'Y'6''M_%'__''''__,h ., ^_ d'__,, ,.,_ .,' ' '' _,,, ' ,, ' ' g__ ,,''_,,,,;_'_,"'"'0'__',-.'^'''P'" ___,.,,.0.,,,,'' _'' __':'=__g'_'''g .,_.''_'' __=_._m_,_,_p ''_' ",. ' _.=,..,=;0...= _w,_, _ '__''' '-' _^'P^'_'__'__,,.. _ _ / g __ ' ___0_' _ __ ' '____..

>'"'_' ''' ,,,0•_''',__' _ , '' , "''_ '_, ,. ,,,, ' ' '' ._'__ - ' _' ,, __ '__ ','' ,,_..__''- _' _0 _,' '-_',.,' ___ ' ,.,__ 'a_',,.,

'''

_. Set up but d0 not ev_uate _e _tegr_ w_ch w_en ev_uated wiJl _0 ve _e fo_owing _ea; _e _eaof _e region inside _e c_diod r __ 3/2 _ cos 0 but outside the ci_cle r __ _4 cos 0.' ____'_ ,, , ____,. __,, - _ ' _ _r _. _ ___ _ _,h_ - _. _ ___, __q___==,,.,,. ,,__ _,. ..,,_; _., __w,_,,__; \ , _ _ .g _ _'' _'' _%_u_ ''''''''' '' ____ '' _''_ '

O ,. ) l_ _,.._',_0._'_ _. _,, __''.o_ ,.? ' _, _ __''_". , _,.,,___'___''_._ ''''' _ _, ___...o _____' & _ ___"':''':,_ _ ' '"_''' J_' , ' '0_' ____.. ___== _' - , _ ' " ___ _ __,='., ._ ,,, .,,.,o, ' _ ',o. _d,__. ,, ., J_ ' ' _,= _'_'_,,.,,,, ' =' '' " _ '' ' _,__0._'_ ,0__,.._ , ' . ,,,_'''' '','_O'_|__'0;__=_' ,0_ '' __ = _. __,,._d__,_.._'_',,,__ . '_'_,,, __._'..,.,,.,. ._, . _v ' __,_,.,'' " ' ' ,.,,_'_ ' ',. ' '...... ' J :.'_,_�:,,:,, ;. :.;n+,',,'.__ _._,. ''_ ' _ ___''_.., ==,., __ . _ _ '' ' ' '' ' __ _'' '.,., _. ,,_, _ . _' l, .__._,,,w.,.._- _,*mwwm_,_. y; ,._ _i_'!; ,.,;,_,,,n,_,;,;_,, .___ _,,,. .,.a4_,%,_;_mxv.,4,____,____A___J___' _o "''__"''_' '''___ ___M^A"_. ' . _.0 _ ='_. '_, _..,.a; ' ' ' ' '.',.v. ' ',,, /,_''"'-'' ' ' __ ' ',, .,.,,,,.,._,_0g,'_,_..'._', '_'_:',,_.? _.,';..__-_,,. .,,,. __' F_,. _ l_ _''___.;,.,._dd;,,,._. _'___e_''^"'____'_''__'_d','_?_,.,,,.d.,._,,,,,___,,. _ _ ,_ y,,.,_. _,, __\ _q.... . ,. . __.____'____._...._0''_' ,',.-;'5;_:_:,;_';.:,_ _,_...._',.=__''''';.':..';"'::'-"_,_,,,._'_''' ' _ '_^ _''__ _"a_'''__h _ _.,. ,,=_,,,_, ,0,., ,,,.,,.w,,,,,, ''9__ ' - ' _-_0'''''T!'.'' '' _ ' ' - ______ '''''. _ _ _ ' _, ' ' ' ' o. ' 0 ' , _ 0 ' ' _ _ ' _ _ = ;d,.D _ ' _',,-. _..,, ,.,, ' _ _, _,.... - .., _' _ '- , _'_''_' , .,,,.., ,. _''_,' _,,'',_'_-,, _'___; _' '_'_' '''_'' _, __''.'..= '" ''''..''=.;=... __''__,,_,"''_'_;,_'e.p. __._,,.e,.,. _.., '' __ ''' ._,' _ _ _ ' ''' '__"'' _ ^' ''',o. ,.,''' '''. ' _ __'_' _ ,,,,,_, ,_ ' � _.. 0 ' ' ' ' ' =,,,d,, _, ' ' _,, _ _ ' ' _.

,_ _ _ _ _,_,., _,,_ _._ d''_,_, _0 _M_-___'''^ ''''_ m _ __ _, ===__ =.. !' '.., '!_, M '' _ _, _; ' _m'"_ _'''^''_ ' _-^ _'_-"'_ _^ ^''m m'''_ _Pvm'' ^'' _'_-_M_0^'n"_' W' '"m_'____'___--N-NN_''_'m'__'__c:w_,,_____w_,-_nw4__ __,!_,, _'___ g__'.,.'._ '____', '.__ : _ ' ,,__..__=_'''''_ ' ____' M '_ '" ''' '''''=' '_D'' ' _ ' _'. ='_', , g '" __' ' _p^M'n'__q_MM-'^Wh^'''"'''' ' _\ _, . _,, ,, Q_..__n,,,.,0_ __,.,, ,. _,0_g, .' ._,,.,,__ ,.. ___ _. _,, , _'='_''; ,, _'___' ,'__-,.. _,,..,,..., _0''_.___'_. ' '_ ' , ' w' ''' 'i,.. ''' ' . ''''',,

_ ,.._e•___ _!'_I.,_'= =',.,_ ' ,, , ' _' ' ' '.0,, ' _,.... _0' ''' 'a_.0= , ,,.. ''_ _' _'__'''' ' ' __o_' ,. '''-' _. _,, ''___ ., _''_''' "0 _ ___ ' -_ _0,',',,'_a.,_ ,\ _'_,.!_''',,_=, '____.,d. 9 ___,o''_' _.. .,,,,,,. ,.. .,,_''_F_ '_ ,_,, P _''_'' '_:,. __='__,.. _'' _'''_ ,, ',,. '''', ___.,.,,..,__e.,_'_,-___'_0,,,_,,0o,c__._,,',.._. _o._';,! _''_,e_ __,N_ .. ,.,,, '_'_ ' 4 ' " ' ' ' ' ' ' ' - ' ' ' ' ' ' ' ^ ' _ - ' ' _ ' '

' "n_' '_a_4_'_ '' ' _ ' ' ' X ' ' _ ' ' n' ' ' _ ' ' ' O ' ' ' _ _ _' _' _ _ _ ' ' ' ' ' _ ' _,,._ "_ ' ._, ,,d,' _. ,. . = ,, _''_,,,__ _'t _. ' '_,,,, _ _,8,__, ' ._a__ ,.. _ ' ' "''__,,,,;.,_.,. _ __ C_ , ' ' '._ , 0 '. . _ga _,,.,.,,., ' _ ' ' _ _ _ _., _d _ 0 ' ',, _' __ _0__., ', _,,, _ ' 0_ _ ' 0 ' w ' _ ' _' ' _' ' '_'N ' ' ' '_ _ ' _ ' ' ' ' ___,.,, . " ' ,. _..,,,t,__,;-,,_g_ \____.,,''____ ., ,,,. ,...0,..,,,,,,,,..o_,,.,, _''.,.., ''_^''' _.,,. o_;." ;M__,,;__. __'__ _ ' _ _'_0'_ ' -_ n __'o'' _' ' ' :.,_.,. ='" __''D,,_,,__,- ___a__ :0.',,_. ' _ d _' _ _"_ __',_ ' ' ,,=., ' ' _ ' _,. .,, , , _,, .,,,, _.,,_ _! ': -' :'' ='_' ,, ' '

_____g__________________________________o_________________g_______________TT______________________0__0___0_,_/________p00_______________'___________________________0___0____00_t______0_______________________)__o____________________0__0__________________________,00_________,,___________p_0_____________t_0______________________________ _ ___tt__ __t____________________s________________________________,________________,_____w______0____________0______0__0___0o0_,____,_____________________0_0_______t________p__________________________0_________0_____0____gJ0_______________,0___________o_00____________J_______0________________n___________v__l____________________t_______000_____o______00___t0_____rlr_____t___t_______t_l_____________t_____?_____>p_rt__)r__J___t____tt____l___r____s_l__pJp________4&__t_____________J_____f__t_|__________l__J_t__t___Jt_rr__fx_lt____Jtp_)_nl____tl__l___t__)_lnl_r___t____________r_o__t_____D__ro(____tt_tf____l___r___r___t_______r____JJrrr__t____0_0_p______________l_______0__ ______t_l_______________0______p_________c__7___t_____,___0lp_0______________l______t__r_ ___________o________0__0____________)____t_t_t___l_t_____40____t____N_____________p______D'__t__,____,__N_0__0____________t____0_t_________tt_p_______r_________ro_________tl________m+_r_J____op_____________t___m___________tt_f__p_______J_l__0_____r_/_________rr________wr_g___/__r__tn__J__0___/_____________d___l__t___tt_0r____/p__p____tt9____l0of______ct___Jt0l_r______t_________)__0_'_____t______r_____,_+__Jc____0_n___p________J____t________t_____t_____l0______t_0_____J_J_____h___Jr____N_____n____m__0_y__p_0__o______0__,___________0(__mmt__y___mm_6_tt_______mt_______ _______4_________%_M_c____e

_T.H 1372 Mock __dte_ 25. Se_ up but d_ o not ev_uate the inte_a1 _of _e _e4 o_ _e region inside _e c4Ne r -_ _ ___ sin 0 _ 1_d _ _e _' d qua__t. _,._m_ . ,e ' _ Da'' ' d''' ' .. '' _ '_,,, , l..___ ' .. _ ,d. _ ' ' ' _,,__l.. o _'' '_0' _'' ,_. d _0'd . _;,,. ' ''__a, 0_ _ '0 _ _,,' _ _',e_, _'_,a,.____,'''' '__,.. _ '' _=_ ' _ ____ -_ ' '' ' '__a_ ' ' ''__,_,,... __ __',, _,;_0d __,, __,.__''='"'', _ ,.'' '' '; ''' _'__' -''' _ ___'_''W'_ __''0_ _'''_ '_. _ _,.,. ,,. __ _ _'___="' ''0,,.,,..,__ _ __"'' _' ,, ,.0d d__. . ),,. ,, ''_=_,, __'= ;_'. !, . _.,. s ,_ , _ '. . . , __'e_'_.

__l a, _,.,'__' '"'_;'__,,,,=,__,,=q _.. _'___g._.. __ ,-0__ __'_,,,_J_'/,,_. ,,__ _' _. ___';;,; .. _,,., _,,,.

6. Set up but do not ev_uate _e inte__0 _ fof _e _ollowing _ea; _e _e_o_ __c_ _s _side _e c_. _. r __ 3cos0 _d _so inside the cafdîod r __ cos0 _ 3 _d in the _o_h qu4__t. ,. __ gcb,,_,0

O __' _ ,Mw____ _0 _ '''_ ' ' ' ' ' _. _ :_' ' ____ 0 _ 5_ly _'_,=_.,. '_,;. _, ( _ __,... _ ,,,., _ __,,. _ '_-.e_____O _''' .,, _B_" ''' ,. , ' _'' -po_,..,_,, _ _ _. _ '___ ' ' ' ' ' ' _ 0 0 0 ' ,, _,._, ,.,_9 __ _ , . ,. , , __m_ _. ',. ,__,d,,,.%h _,m,_m._c. _ _ ' _ __ .h,_,tm,,_m,.v,,m, _,_.,_y.,.,.,n.,._,_c,,.,, _.__?,,.,,,,m,.,.. _ _,, _ _ 0_ ' ,n._,,_v_n-,,_, _,,, p.,,,N,,_, , d! _,,_n,_,,,,, 2,-h,_,,,_,_,-,,-,--,,,. _.,,_ _.,,'_'''' o'_'_'_'. _ ___'._''=,__,!_,,=_.'._,, __/_,_ __'0_';;.. __,,,,, .'''g_,_ ____,, _,, _';,,e, ___ __ _"' ''"'v' ' ' _____;,;:,.;_;,_;'"';';,_;_'__,.__;_'!___',_" '; _,_;,.._,a0,,,__'' _! __''' ', _ " _=, =_ _ ;.. =. _.,,,,. __ ; ',. =o, _,.,_,,,,,,,,a,, _..,. .,, '9 _0 ' ' ' ' _ _ _d , ' _ ' ' _ , , 0 ' '.. rm M M ' ' ' ' .. ' '. ' '. _ _.,.._'"_''., _'::'_''0'';,.., _',;._='__,,,.:',_____'' __-_ .,., ''g.,,... _'' ''''"o''''_', ' '"' '''_' ' ' 'd'_''''

_' PW'', , _,. _,_'_, ., ,, _,_'' _,,_,_0_ _'''''_;,_e'o_____, '''__ge_. __ m __ ',. 3 _ ,____ '_ _d0a_, . ,,_,.,,, ,_ ''''.__.. ____ _''_L.::__' '_'' _' _'_0_ _''_, ... '''''_' '''' ', ''',_...',_, __... ' _.,.. ''___.,....,.____,,. _.. ,_.0 _, _______,,,. ',,nM.,.,,,,,'.____'_, ,__.0.'__.'_'_''"_''_''__,;''.,__,=.,_-+ _'__,__,'''_'.-.,_'''''_0'0__''O'''_' '''''''"'''_m''_' ""'_ , _

_ _, .._, _ ' ' _ , ,... _ '; , d .., C, Q _ __ ' _ , = ' ' g.; , _ ' _. = ' _ ',

___g_0_____0______0r_____g____,________p0__ft________,___________tt_______J__________,___________r______0__________________J__,____________0_________,_____,___0_____,_0____o___&f_r_______pe_______q________,__,___,________o_04___t______________________________________&_0____+____________e__,____________t__0_0___)___l__________4___________o________J_________0________an_____0_o_____________________________f_0__t____________0d___L__________________________,______0__________w___0__________________t___0_________________0____0_______l00___t________0________o_____t________t_____t_____4_________000_______________________0_______0____0_________w___0_______________l___________r____________,______ts_p_______0___0_0_________________0_______________,________,___0_0____0________________________________0____0_p_'__________________________________0_______l___n__p_______p__________mM______0______0_________Nm00_0____00_____m____p_n____t____0m_________,____________0l___ltrm_____0(_&_____0____,__f___t__r____0g__________n______8___t___D_J__)________t_0_0___t_t____N___________m_00_v____m______0_m_d__M__t____________________________________0_t0__________0_t7__0y___________________s___0______)f__h_____0__________m__m_______y__4lm______xM___m%m____t___0______m_<ln____0___r___9___y_r__w9______(______M__y_______0__0_o____00_0_____0_____00_9_o__________,0

__ _ 372 _ o c _ _ i d t g lm 27 _et _ 2_' ' W . _ J _ _ _ d P r o J __ _.

Yb J _., _ _,, _, =, , __ , .'-''' _ __ ,_. '''', ,. __0__d =_ .'' _., a ___,__,' _ _ __,_,_' __;_;,,.,.=_0' _,___,,''. _'_'_,_ _e ,_,, _'_'''_''

- _ _' ''''''' 0_'' =' _ D , ' ' ; , . .. , , ,., , _... _

_.,'_ g',,_ __ ,-..... ,, '_'''_' ' = _.,,

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8_ _ind _e v g c __ O e _ _ e O _ _ _ th e E _ o p o i _ _ s _ __ , ,,,.. 0 ,_,.a.' ,. _ ,..... ,,, _,., _, . _! _ '' _ ' ' _ _ ' ' ' _^_ _ _ .

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9, _ind _e _c lengm _f th e c _ e _ _ _ . _- _ . ..' C "S e gr4P_ O_ r_(t) __ (t3/3 _ t ) __ + ( ia ) ,__ _ o r o_.;,,__,,_,_,!,'_,, _,,.,!..,.._._0 _,.,..,,,,...,,,,,,,. .,.,,..,,o..,,,,,.,_,."0'''_p,..,,,, __a,, ' _, _ d , ,,_' , , ,.., , ,... ,, ,? , ., , , , ,,,!J _''"____'__..,.. '' ' _ ''__,0.. ''' '''' '''_'''-__ _'''" ' ' '"'_'' _'_o' ''' "' '' '' _ ''''""__ _ _,/,_' _' , ' '''" _ _, .,,,,,,,,,,_-_ _ __. =.. ,. = _,. _ _,,.___. .- ; _,,,__o__ ...._,.,,,_,_''_,.,, ..,..,. ,,... .. , . ,.,,,.. .. ...,,,...,.,,.... 0e _ n . _ ., , , ,.. ,, , , , ,, ,, _.. , , ,''''., , ,_ , _ , _. , , _... n ,, _. . .^ . , . ' _ _ __ '_'. __'..,,.'__''_'0'D''__''''___.,,.,_,_'''' ___. ,_=_==,,=,.,...,.. _.,.,. ..,,,...,,.,,, . ,. ,,... ._,.=,,,,..,,.., ,.. ' _ _ ' , _ ,. , , ,_'''' ,_ _ , , ''

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