ࡱ> tvs%` bjbj ̟̟ DDDD$h,@ 4444$ h^#P^44o:44#o4 W>^D;; 0@ C,##o#oP @ `` AP Calculus Review #2 Notes Position: s(t) or x(t), aka location Displacement: How far you are from where you started. s(1) = 6 and s(4) = 10, displacement is 4. We discussed the sign of displacement. For right now, well say it can be either neg. or pos. Velocity: v(t) Can be either negative or positive. It is the first derivative of position. When at rest, velocity is 0. Moving left of down, velocity is negative. Right or up, velocity is positive. Acceleration: a(t) It is the second derivative of position. It measures how velocity is changing. Speed is the absolute value of velocity. It is NEVER negative. When velocity and acceleration have same signs, object is speeding up. If different, slowing down. To find derivative on calculator, when they are allowed: If  EMBED Equation.DSMT4  MATH, 8 nDeriv(sin(X)cos(4X), X,  EMBED Equation.DSMT4  AP Calculus Review #2 Notes Position: s(t) or x(t), aka location Displacement: How far you are from where you started. s(1) = 6 and s(4) = 10, displacement is 4. We discussed the sign of displacement. For right now, well say it can be either neg. or pos. Velocity: v(t) Can be either negative or positive. It is the first derivative of position. When at rest, velocity is 0. Moving left of down, velocity is negative. Right or up, velocity is positive. Acceleration: a(t) It is the second derivative of position. It measures how velocity is changing. Speed is the absolute value of velocity. It is NEVER negative. When velocity and acceleration have same signs, object is speeding up. If different, slowing down. To find derivative on calculator, when they are allowed: If  EMBED Equation.DSMT4  MATH, 8 nDeriv(sin(X)cos(4X), X,  EMBED Equation.DSMT4  AP Calculus Review #2 Calculators allowed The position of a particle moving on the line y = 2 is given by  EMBED Equation.DSMT4  where t is time in seconds. Describe the motion (moving left or right) of the particle for t > 0. When does the particle speed up? When does the particle slow down? When does the particle change direction? When is the particle at rest? The graph shows the velocity  EMBED Equation.DSMT4 of a body moving along a coordinate line. When does the body reverse direction? When is the body moving at a constant speed? Graph the bodys speed for  EMBED Equation.DSMT4 . Graph the acceleration. A particle P moves on the number. Its position as a function of time is shown below. When is P moving to the left? When is P moving to the right? When is P standing still? Graph the particles velocity and speed. The graph shows the velocity of a particle moving on a coordinate line. When does the particle move forward? When does the particle move backward? When does the particle speed up? When does the particle slow down? When is the particles acceleration positive? When is the particles acceleration negative? When is the particles acceleration zero? When does the particle move at its greatest speed? When does the particle stand still for more than an instant?  A particle moves along a line so that its position at any time t > 0 is given by the function  EMBED Equation.DSMT4 , where s is measured in meters and t is measured in seconds. Find the displacement during the first 5 seconds. Find the average velocity during the first 5 seconds. Find the instantaneous velocity when t = 4. Find the acceleration of the particle when t = 4. (,04{|    3 4 5 6 7 X Y p q r s t u [ _ ȱȜȜȜȜȜȜȍjhh*EHUjL h*CJUVaJhHh*6jh*h*EHUjL h*CJUVaJjh*Uh*jhhEHUjL hCJUVaJjhUhhHhH6hH1 Cz  > g  : z  7 ? t u v w gd*`gd  } L ` UV & Fgdx`gd*gd*DEVWnopqxy67NOPQSTӴӟӐtgYjh,/UmHnHujhxhxEHUjauL hxCJUVaJjXhxhxEHUjbuL hxCJUVaJhxhx>*j hxhxEHUj=tL hxCJUVaJjhxUhxhx6hxh*jh*Ujh*h*EHUjlL h*CJUVaJ"DbcdeSlmnopqrstuvgdL & Fgdxgdx & Fgdxh^hgdxTlnq'(TVWXY&'*,-047vwxy|}ĸjhrhrEHUj wL hrCJUVaJjhrUhrhr>*hrhr6hrhh JhCjhUmHnHuhC/jh,/UmHnHuhkLhLhL6h,/hLhx4vw 'QRSTUVWXY0^ & FgdC/gdC/ & FgdC/ & FgdL & FgdLgdL&()*+,-./01234567!W & Fgdrgdr & FgdrgdC/ & FgdC/hr21h:px/ =!"#$% ng5y-;`MPNG  IHDR/sRGB5IDATx^WLjab:P ͌aM͈()2P9hDSAaBCM_eJZTH-(V>{=q}{|||s^u^ӧO@@'ֆ.@y@:q D5s 5DuC @j @ jꨇA@@Q   @@T3 @Q@TG=<4 f@&zxh @Q DMQ8@9@:q D5s 5DuC @j @ jꨇA@@Q   @@T3 @Q@TG=<4 f@&zxh @Q DMQ8@9@:q D5s 5DuC @j @ jꨇA@@Q   @@T3 @Q@TG=<4 f@&zxh @Q DMQ8@@EǿK hQjg(ӟٳ2ywyo2@28VL'x-z뭷J/6K#oZ6@@ԬUKl?Uj~j* STKN_~Νc]rǏ_zY 1cƚ5k$  @/ =жmJr%Kw1z"Tnź @` ԣUKN~s-]NkNui5:s>Nt@jЪM5jTo_y1bD7^R{7#ޅHZx㍏=YA!P`ꄁWcɳޥɀ͞,ݔ[K7٤f(}fձm*S5& R׶襁4 ' дwϸ=t+=PzZۭJTv8@7l-֗p2ޥ:-edD^; Ilc&h;֛V.h8t- LK@ς47xT5rZst zZ2OsޚKKYeR3!nMtՖ=!_-15W/ڣХQ фУNe짅 أ,$ ,tSU8&V-aEL>}?iLZ=-ž9FuDpߏo#_i|1(Vf->@nvvSmJxM*}vџ*_hQjw/_?wڕeEj(]~&3%j'DsXc)03g6n_z?j+p~2 hZ]Umszgc!DRN8aݾ@.ʘ~旦 'B:ԉ>Nҏ9z¶$:R";&|vydL׳HS"\7|6JdK@1>mO[;Yio -_"m!Mҫ–=ᰪ;pW6vdD_M8%s^ =SKk7̈́[݊OsI.0}j@ Ut޾%]vnmZ~.P-sZ[ 56{7Y;Lofe C}"͡64' ؄giISwҤICB`AE Њ?Hʫ):G@ ؞n7ѵNn;%kC $ТZqVWza R20EVΩKl0 .1 蛙P-knP'Jz!(wHv\8p~L6 P.{_^Yu&Q8p Ճ\XHZ-J=+6:@ ty Md'We)%+V_ڵk@ f?PVիW!lUFt."1w&Jں=k֬" ` F+ OS^~:ȑ#~ک' '/I,A γQ,-`0k,hV-ZrZ\b]T%`=Ӷ=:}4L[&Dқ%Q^=ӬXcC73[ɲ--~bתcǎ5, /SOzӉ EK'V]zo)0ҕiUfA,HR @JR( @,HR @JR( @,HR @JR( @,HR @JR( @,HR @JR( @,HR @JR( @,HR @JR( @,HR @JR( @,HR @g>}zС/g=~m;vѣGȑ#^xaS @^no^/B 3Zʕ+7nܘ!=/ 꾈H@m%TTнcǎѣG祉K  RO^@N5  NT}ye1wY @m%HTo޼k׮0aҰ ~A%HT_~ܸqtoڴih%A@+ ;w`޳gϊ+LfڵK?Jt  P@ښ;ye˖Ifq^/\P @n .YDK׺s~5SLYx矟εf͚~x̙=\2I @F6QjZfpĥjW]˭޺e˖DO?{޿og̘QprA*%$h}swTW^mrZo~0-E@6!~_]VINz޽ KrQ{YgV︗^z馛nshx̘1v֎ a@r Yoĥcґ#G76ZVʽ';*%p=֤U!ե|U 8#@}rQ2$sMJwL*u묅2 ЇsذaB'm&Vai P@ wy޳ٳlFH@\$@f ԣQɝ1\/V9&A} vn*:bAY˱/D@:H_VZN-H ,C!e6n].*bA͚ͭl>m#*SeקnScxF$@$BT;kp77EK LӡmMff^Z֑rDy15hv*48 K.u5akT-ӷ L\tEbtQyS$Y P j_xh[oIe`/dFo~aK~ChUj+ [dno.@D7I^.%p)ٖ ΓX&fQ8(Jmĝ aVճ4d}[PӒ֒VG}$i1YTc/;iUjyJ5G H|:F\_Yꉐ%M7o[# h\e'6!jBΛLЩss!_3g ߸q`d@vgc9\Z(TpiB SRBmZ6js;2x#8íG\wuY&z!*QrF;1Er@YrS۷@i2LK Z%JMVnhF}fƌm雋K?O̾Np=$5㸹y GT*u.Rz[ C8c9`<$y~'QnI'eݕ+xlUVUt,GH!}>sLlK%(&QcJ]Jm]P'F&Pw mH- yc /\E%Z:9~o.ҌyIXRbTMXfpyó\ @D\RچA۵]DBV75[_;D:CfVjRK 6jlmRr_L,"^UBK[1\Ϡ6awjo1Ƌj_v{@0woJ)Mc9rX1\/JDکҧPfPe0[S;EUZe ׮k5/1hJ2bq׊6r*QSƶ@h=̒M=g g 㠸f+NCGt.ȑ#~{M3|?O"KؿlaUh6(serțh+kYNX]HM̸0yїB-}qg?-۸n5;@ǂ@SE6Rpi]-oJHw_h7Yo&:)G^Qѕ8(j 4UT;Zzk3i(Ceҹb#<#cG$ihHZtdAGt$HQ.I]GDqGꍖ0٦>:[}nev؜9s υ0վJ qF9nG+M?Cr:IfXKvpm_zM0M'eFsԵ67y5Ԧ'8o2mjı ҵOiq8tː}Q+W Yc&ǦRz9٦nQ N@ʬ&kzw _6;O:=#  70[W_mg1bD?~Ϟ=!k,\WDGY}Ep6nIc@.msKps -9 c"c Hۑw/b-ݹՀZUiDs"\mOP[;r J@F nto(˓ dmI9{ɒ%ׯ>]kF 6LTEDLѣG˭_Xev/^(O%F%}mUNo'gxrbkLhme~ggΜ؇zhԩ .>Eoil߾X`!9"Ѫė?`cIE۪[o@x$Zbp/c?s6 ++!}饗JNd-;f%;Ç,XNҦM&۸?I)w dt+M+*Pt c u3c˳4Ъ+ӷ;C0ڏ t~Xzb%0$r=:h6P?ΞJeň7xC->}zXgٿVyKN<ٻw'L;DRow.EڵYi>+S H͂@v [jh%ڎR@iRO>I'}WfQi.{@VQ3**7KlZJnCU&FoK`p@LN2߭=YY4uj"B>@` hQzi *S3J;ӛڭ ZK ֟JОM+ٽE|=[K:{[øeoOƔKɘd%puً]-96P(\UJ2;NqG{{ڄ{4-};+wFywW :u"S2`@hBnչU`kωd\6tmo7u*RnK^8RB4o }ʯǾ-W\LtiɆXH-9OXKvHGك>ކBQ˖-3MIMN,판'fo|bH)eVSL W^?5C@dمUix&YuFVQM:1›P?SiODkoU 9pDuͦjX* pQ Pݻw믿^'5kVߦj(!?ssm,ٮ]|+,~Wئ|)f'p R&y.PGFFoM>HE u+s]֩6b.v ;Nl|e?BqL4gF'ꎛ])f :nK̻[mв, Gq߇\iJp[FL5o2J;vu&Ɩ[]06ʘ!KpTkd;rHv@zZfֱT\pVUk5O#q+TRT~9H,5رcJ֭aR}m۶5CVOb^ۆk;Z/%>uѵTC3'墕 P& Ŀ$0\eԿki=6UWuYSt|spsIa3*BgL EcK"y;0#oR2Gre/~!Am_I?vpPI u]'O%Kw׫L}s՟YZ-y5fݺUf}g r$}4N8aSL'BOiNbQͺ,)7V],UM|a/6ٺ2g}e GE^SQJ^7PM(l ٯ1M!@,#/i_R:zX|DENHxnij٣=ZdP_Zk3|~wLl-ե&|%D 793=h\Quʶ:4ZTۧFYaDpa9, @-RMejTCT?P;d.Vu5A",;g/V{oyE. 1YgW&tmiMJN2=E걘^{~E΅p̡Fe}ǟ}2Qw]onbmQ,_nذX!R(DuG̙c[ ,֭[,9{8*=J굅n@T'N,]6*(J̡F.\xƄ>7n?Oڪ!ɭZX v [W]uwy;wԁY)&Lw CQ]XK$XYW‹ڢvIIֱ5,o{t?f$9׿K_1o!Wp(WixԩRwXSZ7v#5k>}Gdl@cՕ7"gۤuӯ^{ͺ`z]栴v\:q,SV"22)ժ z_W6@t^(4+F.ԨlK׺u\ T%@5U"Hѯ%.*HNkǭ&L$7\"hVQ'ٳg[=Ǥv7R˽) ΕSI'NmT-y?V") Dut0T\bmdR0#`뭟룏>Rcc&sΝ%<,lB[U=oF;$ߺP."!Ј3!,ur|fk47Ѥ?$U}fr ~YW~|>;>%%M @:JN==x(TZJ-DBE+L-/'5ow"?MiҺܶ]E:3<}aFEL&G3ƎkABG~Cuە6)eh2NrGһv4cǎS_3fܱJg".Lxǎ BxYW۷Oe5r Q}8tkLS b}E٤ Ewp_!.p]Ғo2_ ٤,v5ZuD_Tq ,/Ɓj[$} v)M$k&M$?pI Wㆦ5/6mٲpCB Y+6Iö7\ (rig#F@ AQה: 0UX&*ʆ :~a%P!_o]~bY9*j: B:Kltlit,:M.<{KJ @T8TK.5ZbPF)rBE@$Ց 7 B2ۭիWU)9 p,Gp@AՑlLrZ:VYEmdEKW HGQ)ֲXW:N7յR%K,\zthq#U?L59=w  DMQ8'd2,Wm]:^ 'a%ȿ(BSL:  PYbDDD)u_z-@`AȫS-Z[M.V)YMYC0t$PZ:[>Axcǎ=z9rĝ]Hޅ-OG}B;dYw?t,ND.Xʁ P.ڴ͛7_kΜ956Bjl lܸ4$Iv@j׏̼U;ҰWZ.DfaTokrD544H.\d FIRZӑqtL6o$ JP+=<' H@P}$  H@&TWzx4N$T H@*M@h$  H@$  TR]8 H@R3  H@4ãq$ g@$PiJuG$  H@Jπ$  HJI@j H@@ (Օ$  (>$ JP+=<' H@P}$  H@&TWzx4N$T H@*M@h$  H@$  TR]8 H@R3  H@4ãq$ g@$PiJuG$  H@Jπ$  HJI@j H@@ (Օ$  (>$ JP+=<' H@P}$  H@&TWzx4N$T H@*M@h$  H@$  T@Rt-[',b$0>9zhYݵk ٳgˣ^ H@@j޷~u]7Jsg}6bCMۢ$  H [o?keRH@ F8@(5׊+¿\pAp-es̙4iR׾MU{+r>-~g.>Q,|`Ν; k$ lYkkԩx]> 7bJ~ᇝ/?O<F!4 +.*Cl%t_ $ R =&o7'NS3Rx|O>پ}{yh> _^y̧ܹ?S6z-Z(_=ȇӧO4i޽$P5 1ڠhO`s=wȑ3Ա_ڻKVgu,_|N:$VRSO=wA|ǎ>Ӯ*v=X$\ےF$۞}ٍ7T? 0Lˣa(72~ln'Nlҡ$iJ|㭅St[$ b<-Ms;dZؿ )SLlEH3!@,} |@N?9m6:׸dɒw 9\a{իWOF>|2gy@-  Ke0mX~{C>V 1I$ll]@F,C3z.XL&^Ȼx\T° ᯘol'L ɸ:G'|lݺs&uvr_pٻ 8I< 6TxSbY[#K!P̏?F6*f1aVp }jk<~Ew0" CكG롇*mI`|iˋxoذܭ76krou3&1s/w6'QYk+Fyc=СC'|(Uy$J`DDY׮ź'"o}f8^VU$H5SYf(# ȶ$ b&f; ^IҪ7."tj{c֯_u. T@B9TD&k T3u#M@ YBgz͜xJ&hF̑<`-EwETN'= ,<EF\܂Xn]ף I`DjgyիO8O֪W\mo%p'/_:$_n3D;ʶ)Sy&N˪# H0x,(nBQzoETzV]F! A\u<:'T%  H@CPeQ H@@ۢ$  H`J,* H@(R]Sj{$U$ R ըrΞ=6* H@&&g}v5IU/׏3. H,%u*OZ@ +я~m(XLӗ/_~'u׈W^T7xcܹUJ{$  4@U\(۶m%JuXhц ݛG}nKqcoַ{۩Dp6kk׮͉lS{:ٳj%  H+J̪.\xJUqVxX=c U[lY\QNhƓ]h޽ÎB3 H@(_IsN6[S,N?s\r :[B)Gtp֬Yr=yb$Id8H[_?l_u%kN3v<#a,)ꏋJ@h2z׮]kǼyzfMOU`%Kz4^@&޺f͚NXG At [l Gٞa&-Y۬j$PwHui"MF][~a-r.]?婍ҕ+Wޏ?8uU( H@ VN/^&Nf%'cI ̧)\Lq}'^b,Ϝ93t]Ni$ *(ZK/4Nzduդ4:.FɲRaֶ͛7F$# yQ$  H@R:tc.Tر8{o5nOUco=nݷ$PT[uHo&!7@iVX~tr lK3VNZ$ ^ +xlܸU9bY 192გ!B#Ore$  H` mٲPKtzYqu$$  N@ PK&$#C-GB ,2YgUH@g.d8e1)$YPbfxP+%xX;ؗ!y|%m3Y~G !\oo<5|NGSEVwaÆPݻwRU{>ԕTFC_[F7DEJ5SòD-5 o,@VGpeE- T+\駟0aBM6mΝEZJuN3O@Y7Ɨo|YYa( /Toڴ3." (TULaeitC8ef ௎yZ" KPN+VRTz՝@k|Y{_cE7:3ϐ"IǙw}M74Pu-/ݍU?֛a*ڊـ %n >묳i:x*~p .7N=_X'v =禄XB~AVKկzjYe a'kd !axM$<]%?-]E_q,\aPy} b;~k׮ŋO>5hO?mkW_}wG;k&1erzHR-ufI@cO in缶 0 S?[W7ğ?s V$CfTTuR }[CZNeSIU@@ MUtD7mr*Aۜޡ@:)t: ^$bʔ)զߨI@cLlU('T0oۿ(̡[UM/Ms֕RsbwVʔ6)(yǰdec.K?PCmaի :iw;4Džő;]'1܇G.b΋OȐR=HGuf[…nuoxhIy`p#|]PcunB8FǮvX #a0ɋrB+f4'ku+UL}6#񙇙7;93<(yPx"ܿ~z;% aA\C7n.,(+gd ʾoV덤7ZO״b7 ~q/+E[v C׬YoQ ns , ,Y2KH@%رc-G 43ݻ4>*R曭$#w^3d:t$)sv~eu^2N+GiȰQ^pLãߤT\u m@A7auD;Bt7Wؠni o!L:WC[¨*<`DY>eʔp@5΂h mYpLۻw/ghM`c&O:ÀD̪Yn-ۜx*|;1*?OZcfPaLͷmS|E?!/u]qE>+ZH2JY\R/~#qk?#_Baޥ^9!oΜ9%{WaeM^s8=yK2eSQזDZaeXHp. +ޘD̟ +l0gչ5Rܭ?YbV\ 0fixV 7@GX-/4{7 գTR{"U<5մUWGg,\^׫#Z[5JuFnE_իWz衐s4E1ߞG^%7x(lk{}$P.5c4[r3I_aP, VjX"Rjœ 7x㷾-!lٲeMӟf-N[0l%m8,gPZ`a&ܨuc˅߿h*z Av^rm#P k%)~;O-p.`t*x =<0uy-.Txqm7ʽ_TM"89G$  ԚR].XsK@ (յ>B8۬/crzI@/c= ,Zhe>(@ #{ 4Zw_Aq{WBM$@ 'kw_8L>\F>':s&OC*a,6O\g1Cd$ (Z8p饗N8q޼yڹs'ǰԩSU/|Ju*Lzљ3g cV^}=T*m$0,7&O||IVzq| @Xٲe)5k]2>@ VUAvM7W_}c6äm@J#G֬YiPp{I >l2Bh:%  JP0a´iz礓NʵV>U_{l<{-Z(TZpaQj|e N<ҡp/ H@5"P &𫮺F4F3Jx0CL$ (_I._.ȴn_6iҤcJ~f GZ=aoާq֦MN<8p{/h/ p,^(Z `@Jj=[2I")X oRk-H5\-X`Æ 6rp԰r038 qqΝ8{%:K% I xn{g͚wsimI oJuބ_ȑaﵩsm%PKo@F1pjTZ5@ l",\Kp",E="jP9.Z% GfuPkvZkƍUai TR]Ց. H`H%()HZ/^]Caq TR]Q& H 3f0p;֬Y*@u( -2 vO2*$P<, C ;wn5|V A@.mH@@0Uxm.[Ju#C (@ H1Xǃ=ikLHM (58͖"К*kȋ&#T'd) H`,XpriSWJuEF$ r A͛7k-zlގK@v$5{H@.MK@U'ЪJ.G}Fk_(ՍR;$ dJYݻv{d P3$0/>w=L>DW ns@- ֯j<؃T/6Ux-DzF+54M 7nHXj]P]%K… .]:v$PO5n`>{ T:Y]T?߿NU{֭[zu@"3~cOE9(M8bO=j H@ jڃ=rm_)M':jJ7x 8rI'` Čp->p<;v쐕2'PTG|;c &-:=^y"p9ҧw/ buq4]X" 7t'MT! H`F!AJP*}\Tv+꧟~z„ բߨiӶlrWlڴiժUޫ* ɓ'_p0VM-a2Ze;+ 4iGI> ;JVa~Nwk׮:k۶m6l ] g^ ֮]۵jѢEuQT~t}g;& T:: 'q&#ý;}ߺug]_߫E&cD#1GͰUqE)5Owxo߾SL !?`rcK@HBpCC˖-׿B?n&7+U=]SNe>]Nc?䧟~' >cIt:t([M@VWpi:rZ>ᇮL:HsĪ:$Āq$c8oOmSj s趋[$ %N>d>ʤ2]݁q6]䆋stW^C6vמ-F;3IcUgR݋q<3mY(>+vVh6|];D}^{o>&9a!֙ cw3^{V"X h$  4w1cƌ!ҏ9REojq켨U.?bOHݫR= =$Г! D}AuAl9 d;iPzWέG2[n,ѻj J!Br9SOvgPpd[vL-S9%磰c2vS;vH[me]!E=0._ӧghxVUT'q{- H?t1u ' x;#99YBYSJdS֛ѴR݌q@/_׮bI&һUN;nhgfαSyB@J@ȅ@r߿k6p-Ј"Sg>U{p;<C{WSϙ3v\9sbsOZZ H@ 6kEĎ`z|0y䮓+VlssqC(Iwqx`Wjq +<].Ue7M"gVdC1Wa/ƅXYf:bRƚX[9:U2JuJ$P^NN6[̪xSWF۶m3gF` aZ$ pK.MQ/+ٿ/~_͟??n!gڜv˵ aZ$ \0OEw:2;Uz5@=z̙CF'U I@(]ӖaKڬ|ʕSs%SQOE@i<1ΩV+ H@>z̪Q %  H@9Psk$ l(p H@@NZ$  H Ju6E$:'V+ H@ȆR Gk$  D@ J@!TgZ$  H@9Psk$ l(p H@@NZ$  H Ju6E$:'V+ H@ȆR Gk$  D@ J@!TgZ$  H@9Psk$ l(p H@@NZ$  H Ju6E$:'V+ H@ȆR Gk$  D@ J@!TgZ$  H@9Psk$ l(p H@@NZ$  H Ju6E$:'V+ H@ȆrIENDB`n-9\=}pֲ!%PNG  IHDR(sZ@sRGB8IDATx^]\qBR_.H}+MWjH%$P1U(U1QZX/\=o3s93{E89g^k}֞g˳߷o~>P@P@a ( (+`u ( $0Jm1 ( (׀ ( (H+( (^^ ( (@"D ( xy ( ( A[ ( (`5 ( $0Jm1 ( (׀ ( (H+( (^^ ( (@"D ( xy ( ( A[ ( (`5 ( $0Jm1 ( (׀ ( (H+( (^^ ( (@"D ( xy ( ( A[ ( (`5 ( $0Jm1 ( (׀ ( (H+( (^^ ( (@"D ( xy ( ( A[ ( (`5 ( $0Jm1 ( (׀ ( (H+( (^^ ( (@"D ( xy ( ( A[ ( (`5 ( $0Jm1 ( (׀ ( (H+( (^^ ( (@"D ( xy ( ( A[ ( (`5 ( $0Jm1 ( (׀ ( (H+( (^^ ( (@"D ( xy ( ( A[ ( (`5 ( $0Jm1 ( (׀ ( (H+( (^^ ( (@"D ( xy ( ( A[ ( (`5 ( $0Jm1 ( (׀ ( (H+( (^^ ( (@"D ( xy ( ( A[ ( (`5 ( $0Jm1 ( (׀ ( (H+( (^^ ( (@"D ( xy ( ( A[ ( (`5 ( $0Jm1 ( (׀ ( (H+( (^^ ( (@"D ( xy ( ( A[ ( (`5 ( $0Jm1 ( (׀ ( (H mݶ|c9O/}'?$P@P`n.^7p9ݻw8O<׀ ( (и@/W^}Gc=sa}v~tơ ( (Б<>*wI't!= ( 4.НOF駟.kժU+[P@P^z@;e]fO+ (mNuuw}w ( (Щ?uE\+d}ݬ ( D;#^G9ꨣ.–([ P@PS#^Ew2k.{ ( (@3ڽ{}*e+)Hޚ%Z (PQkW_mU=L CP`v79䐁)97p?cFwvTV^zի:)S.9>M6s1c;s CYLVRyNawVtq&Wl)@w/,Y [v͛fCg~QK/D04 P񬊵:c-Z4XV1=&6|#WrFر㮻N>db_a (ՍDzeˊNeЋnV(B!=1Jn_|eݕ'SW wU)AqߑSy_T(@o:Ƌ.& Ă*nU.'&73ǂ?B2Ƽ$!)0~yy=@* t$ڸq@^7VK/ݾ}SP@P@y:5o}++"y<@P@X@F/^6o޼hѢ4p0P@P`R.^XwqO?G9+ (3Tc6~f})o* ( t3O~c`gk׮Ii<^P@@7/-[$w~?;wγ) ( t6Bᬳzc"i&.|p"V@P@f( J[fP@P@ ڽ{7Xlܸk ( (x!J/;P{v>P@P@d"bW^,g=A[ ( (З&(gպ>'d;cP`RLz!r5<ۗZ=ڇ tLkexk2AV{aζm[\X7Wy'rIdɒݣPL#JcnܲHh=+;.ڻkc葀#^ l2ό`(@wnʝ0ʭ15kwqHa|ʑLKe腀_|q, /Z| tQH+8DZDQD]c*̵g]qtzM}0ZxO3q,_g9`vy` (@ޢȐ [ؾ}xT *a (Xk*py1U,`y>Yୀxkx[ (d;^,/OVfg苀״=[-^"Kn?W 70459Afg53Aܥ(r^o fpmF\|eq (nrC>fHRb mw?X;r0Mo9._pwQ1!a Ϣ@6 >As΁Clٲ$ 3%iq ~?y+S9YwnwfQ1G֯_{C?U&3j/8|.W_sxM߲OZ9t.Wp dnO>dgQnٙLjN,_j-X^$7,ұC8iNΧH4iJ5GW} )_iT%ƵMh5Pʷ.ҊqkNй#K2 ;†'~+͛(V}k`#|'EDhBҥ~)^!:켐5+ihl+ J!ZQ򬹎k>SN4e#fUә 0pA|e#oy3yW}E= -{pk׮b :m1X(AD۫om 룀W- |E&g^KTJEiӦ{$ؚkMÑ/kOcG$_)olEz.&`Uix-/V0M/&W  (ٲe}y3M5pt5$V}1b2VAs[+߱{| T0ĴX\{͎9@/T>K(u7"jafkȾbGF\MX 'Y,H~ xY3EŰdwz (PMhơ,Ynjh2=ǷZ Er/gKIƨjյY ;+W/g}qn-e-/&[Ee0ՁrY 0s&x1M5L1=W|_8~rO@H੧b[hьNY4skV~dY#·"4߭7JAo |S 13"F&b E^ F@`'ӨGy'hshjSxcuQۦx_+JTQ,fŘir3vY:;`2P  mS&&.븻c]M5?1hkGx_+R3c`aD7n AA@6|9Wd`iDֱE 2^C6ꫯ>]'|k!6ݻx:h}<_.TVTk`y @ …!"U! R 吔,²¦ߍ7޸f:8Cy8sv4jU'.n@n%d,9[72P OFIDw1|^uuuU$a}i^z|mgjfz96uoM< K@$,!'=DrC:cYdoY61 2$$wYf$}UV ~Br~C ƀYqӅ#ۈl$0:zf`wR G)qR$(ӳl6tVċي+3eƴi C>SFB .H駟5W_ d((O,eW]裏[ouV_> Gri/Ce/K{ˇ_Nu]wYC~YUZ1x5L‹+>lbXl2 TA&ʃ46]U.2Pt/lzh %{m׿rgQI]Nų|MV\e#!I'T_g=߱[wr7lPLe2wwV^"ldX5u (c*~1iƜF~s GN}{_'B/(k`lrqʇqNcmЉK~<9s|R@欗냕lVS9̊l`z1yrxauOTs'Y,ђXכS@sSu1 V%ƴG"xe| DT8F"8+X]y\%1P##HӁмǿ+x p[÷&:QXoӬyLUBA2cc3;bdBw>Wi=}WNm&ybm}Xc\&"1M#'I*~JM]O@bd^tE'=S ߳>/HrԑbxK 8 $Ye +x]/Ν|WKCdʉD{I$e@4qSe :jD1{ }mH=Q}.+i_zrDEvꩧ#237tSFC$g+!D#d8<6op@N;~;XUNt˶\ p2Х =e?tɴx:g|,{'"w l~,x =wb*O-?_[rgR"^i2/Lљ+ *nݺup~͚5X짌V`.gqO#8<:5&2*1LP2TWLJtAu͵6!>f/Ÿg^YKXḣ77^VDU/_fvǘy~ǭvUʷDZ[IX M4| {XԃSl߾=kZX|#Iݘf~ٲeVe0ac ^la1r^evK]q3zjL*|@~ #bqҳ}ys9NZAW:s yYCgUh3 iv/"ݨ͌5<^5V=mktĐ^["x\i5Dv콣X&k+bXp~@|}ME@פ靚iG.EG6ҽz-x5.A_xQ"qLd/1/oZѢ_ cMeGFcCF6?ҦbYC\ 2މgpS~t #v\o|\і\>c4$ gSF^1P14o>e( 3F!`F~>jvo!Ͷ[c17(,CY[[X!oa}/" ]y^bu:_&$?CĎN8#J_@3k;Fɭ3(R۟}߉6ħ??|  Ikb.dOJgշʕ0vHw>6#rC082 ={kғ7rwM#⋑$)E\ӣd*Ϩ-0_$ ;2jH[lI\s &@%j-.x!S90;vj;kV2W+mg5qSbñE6#s.Piv_\Ts =PqFu51H؂|8ezVDrNv dKcp*"/ ˜ cGj`%+f]$53['9YX25&R3 F^j;p5Hڪ9.(GcފoyV3;2|fhB<9ӏhE'. c'n]È_MSGMxQ/H-Q|1Qge+;#[Ks"\p:fؕ!*]RCH>Șd/;oe7XW`` xU)# <4^5&Z?  1egF2腘؊xsnJO{W9`d *hV9mqXl`>JD3㰘n$zz%j!XIn*Wc+A"MIl2 ": ,Ӑ%&c}13!`UdIE]|a1S0ed*d8$-ƝZm|ؓ8|? xn>hMa,xf;SfWT E.hޓ#t mO&M6'aEdK*b/*RKD94k^\? WbXMqvY.Dw53gKh`F{e{#ͫR `1JY|vFcdɒ7x#AK^'x$ JYAInYu,2Yq[ƒ} fU)sNy>|xQg}ZMS.)U8is|A_ $eic|ڶm[#Ю xug-#>3R?3YM6 _Zt%(t"-ZDGO~G?ŋ䚫(7rC0bJ'뚾z3<8%\2s6uGQt7Kصk߳o_T{ymذsW'u?׳">/4eךQ|rJj*7i{=wd )@+VrrC0h\ɺB ZXըҘPV #+-w|v7>:r&̷;xzU[v7o^%믿vuqf{!;dq8R`7d3 h sTqϞ=E$؊*ОsQuqmmOjr'FYy睹*yGsU,yFޣXEwp- 4-'OxU kSzuƊTQ9*XH5W^ jǮ|;1rC TaQrC0[W<&vA址s3}0 gRģAwq?#7 o`,ou\R`X]M^|p"#O7j3| JsbCYQWFI R" !jE9R&/*s;—:^/9Ƌ<%{rquLyϴ :3aќ;Lcm ˏ:1b`;vZdEͧzjvUPt: ؐUޥ; WZݦ\m<蠃8+0٥2}Aԟ!^W.t=?; ;e<>裨@ 2Zx]!d `t4]|ZfM}]^E o1%\35d>![,cn:cs]W.rƊEc-0ʿ'i멋eȬ a&9ǶK`Ν\C-[FUgڰ_2bdc/zܓ6]^U:s{I!"*L3{F"䊩[\׽l YͽSWXô#k(F[SMneV*TYd}P@ ǫ (Xs*IFL˼bW]N hS] C ǯl +X8ߦZP@K獍#V#Jrmٲe&>`dѨ+eX (Ь#^gP:%+VgPhn-Yh#^훖Ԍ0#!ZR6T#rC? @m&렀 4%`Ք|NÑ}uE g4Ԙb"7]E9܆ A* (xeIm"3ׯʰ#GӫKDYEr<-pM  uP@pW]YX*nݺ4c97Uܺu+?{Y2] (PW]<=sjzv> MUwXP`^3ѩ<%X}aUd|{>Udt V?㳳o6S^I$`W,i"bx~3DZwqQEEuuyUR@Z(I 'hu7KMI|$aֶmʻ#$Zj}Mh@7CxQ:#^EzՉ7|?Y3=wMh@7gxm޼ygy< ʷ| g+P@v t3"s#dcGZ֑+Kk[P@ \P@蝀{6XP@0jJrP@Pw^r (M x5%o ( (;u V@P@ \P@蝀W+ (@S^M[ ( Nw]nP@P)-WP@z'`ջ. ( (ДWS򖫀 (0]`P@hJ)yU@P@ xm ( 4%`Ք* (@ z6XP@0jJrP@Pw^r (M x5%o ( (;u V@P@ \P@蝀W+ (@S^M[ ( Nw]nP@P)-WP@z'`ջ. ( (ДWS򖫀 (0]`P@hJ)yU@P@ xm ( 4%ЩhrP@P@y:x]^wޑG9o=@P@H,}iq ( (@?:5. ( (W.=e=P@P {( (@.^T@P@ B (xSSP@0ʾ m ( "`KOYOP@^+. ( (W.=e=P@P {( (@.^T@P@ B (xSSP@0ʾ m ( "`KOYOP@^+. ( (W.=e=P@P {( (@.^T@P@ B (xSSP@0ʾ m ( "`KOYOP@^+. ( (W.=e=P@P {( (@.^T@P@ B (xSSP@0ʾ m ( "`KOYOP@^+. ( (W.=e=P@P {( (@.^T@P@ B (xSSP@0ʾ m ( "`KOYOP@^+. ( (W.=e=P@P {( (@.^T@P@ B (xSSP@0ʾ m ( "`KOYOP@^+. ( (W.=e=P@P {( (@.^T@P@ B (xSSP@0ʾ m ( "`KOYOP@^+. ( (W.=e=P@P {( (@.^T@P@mjQIENDB`Dd @b  c $A? ?3"`?2[MWw3om^17D`!/MWw3om^1< ( xڕR1oP9MI @C%:EXtITlUx"*)LL eS3 *fPOw}YQH]ӱmAM j\dt鄁%%[Ȱ!K 9BFѻ_veIJ>%褺Moj#S2u-y%_z.stՔcN-++,Ag>ŪN9IԢET wM95a"yIRhqoi **kśnl6,y;Nqgjmz{u8MTyk6˫֨jVÌq61>eb8ڰe؛(Y?d`e 34qxq3u5%y@%PPj=Wx`[S~=dmsd&'#3\o9f 9mKxJ}aO毻Dd b  c $A? ?3"`?2$f'؃ b ?oU`!f'؃ b ?oHxuR=kA}KlF&Ia,$v#!")/$KY1Ƹ9@~@.ƕKw&}H.U $ nw%D@rl(@$㱏6h%؋i\L"4b,Q;#Ʒl#>ghC g K>!ђxI8㗃+^7n R[M>ܰ ~9:~32Ipʞ<;'dZ K2s?sRxv,~)ۻJPEZm_F#ow 7N~tWŕZh;u#j)ױB:kŬQtm2*??bL-FV55ksmǻ 5h -F/nN7't6RY>YʉO:+aLu9M.q9MݷstV,_(2Dd @b  c $A? ?3"`?2[MWw3om^17/E`!/MWw3om^1< ( xڕR1oP9MI @C%:EXtITlUx"*)LL eS3 *fPOw}YQH]ӱmAM j\dt鄁%%[Ȱ!K 9BFѻ_veIJ>%褺Moj#S2u-y%_z.stՔcN-++,Ag>ŪN9IԢET wM95a"yIRhqoi **kśnl6,y;Nqgjmz{u8MTyk6˫֨jVÌq61>eb8ڰe؛(Y?d`e 34qxq3u5%y@%PPj=Wx`[S~=dmsd&'#3\o9f 9mKxJ}aO毻Dd b  c $A? ?3"`?2$f'؃ b ?o@ E`!f'؃ b ?oHxuR=kA}KlF&Ia,$v#!")/$KY1Ƹ9@~@.ƕKw&}H.U $ nw%D@rl(@$㱏6h%؋i\L"4b,Q;#Ʒl#>ghC g K>!ђxI8㗃+^7n R[M>ܰ ~9:~32Ipʞ<;'dZ K2s?sRxv,~)ۻJPEZm_F#ow 7N~tWŕZh;u#j)ױB:kŬQtm2*??bL-FV55ksmǻ 5h -F/nN7't6RY>YʉO:+aLu9M.q9MݷstV,_(2Dd b  c $A? ?3"`?2P#{:)Dg `!P#{:)Dg`hnxڝTMlAf@uF)-NQW%8IlɃݣ7wk1)]Cmt͛7{ .@9949cb,;a<7[2B̐1t2d~ 5|nk%:;l];_ HWf"uL|4s?7"ma7kdUھ޶mǔ͡tUV/iur)& _3Y^%9K?fh6Gm6pE 2ƥ،vF+x)~>_@'Z=o}ڿVGl>)sזՓWY'/0''3(ȵjXW 7[Z:G+,D^U!Ŭ?ըULuU9:IO!UIȥҧs zېz@|:̥tĕaF`%QFn #a5Y5EбCa<idʈ4|fMnD2Գfߍo^G*78f)kH1G+Շ>_9uDd b  c $A? ?3"`?  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijlmnopqruxyz{|}~Root Entry( FM\>^wData kFWordDocument'ObjectPool*K>^M\>^_1287229463"FfP>^fP>^Ole CompObjiObjInfo  !"%()*+,/2347:;<=?@ABCDFGHIJKM FMathType 5.0 Equation MathType EFEquation.DSMT49qLDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  y==sinxEquation Native _1287229584 FN>^fP>^Ole  CompObj icos4x FMathType 5.0 Equation MathType EFEquation.DSMT49qdDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_EObjInfo Equation Native  _1287229548 FfP>^R>^Ole _A  p/3 FMathType 5.0 Equation MathType EFEquation.DSMT49qdDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_ECompObjiObjInfoEquation Native _1287222333FR>^R>^_A  p/3 FMathType 5.0 Equation MathType EFEquation.DSMT49qJDDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_EOle CompObjiObjInfoEquation Native f_A  xt()==2t 3 "-13t 2 ++22t"-5 FMathType 5.0 Equation MathType EFEquation.DSMT49qJTDSMT5WinAllBasicCodePages_1287222626FR>^!U>^Ole #CompObj$iObjInfo&Equation Native 'f_1287222625F!U>^W>^Ole -CompObj .iTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  v==ds/dt==ft()m/sec()() FMathType 5.0 Equation MathType EFEquation.DSMT49qObjInfo!0Equation Native 1_1287223050$FW>^W>^Ole 5<DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  0d"td"10 FMathType 5.0 Equation MathType EFEquation.DSMT49qCompObj#%6iObjInfo&8Equation Native 951Table#DDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  st()==t 2 "-3t++2Oh+'0t 2ƤyIbnz`!ƤyIbnz(hxڥTMhA~3dMITT҂ z dKmJ0ÚlH)ٵ11TA`oBIzCHIA."6l~mRuٙf7fm @ac؈FaqrsӖVGi" C H8RG:v"m[y ʒ dyq1t\p #A];xP'*ڵ=Ϟ~+?|/?AkTg+XoE_7~cGsor>:qtlqhrGcAczo:GRz`F-.5eq|B ޡ #4sbY9#ohhVI-tx_?=wKh > "id]`Wx ?NCx^R( S+v".\o?J~P1HbǍ|_'>1|.Gr*Z5L+i7 c]6ő .Gt<15a5A`21 I,۶o<&M|2|rgc. W6RzfVyRެhanw̲qϴ 6"y1EVl%D|jn+~aE+;r]?/^@|^): N]G*yEgYpBmY/E~fX 0VL%YtDz65"f!+u3D2X /4V]C< >|UDpFJV:m6:BS5F&{'B7IvkSummaryInformation()>DocumentSummaryInformation8ECompObjLq 0 < HT\dl AP CalculusSFSD Normal.dotSFSD11Microsoft Office Word@ @,U=@*^  ՜.+,D՜.+,< hp  SFSD '  AP Calculus TitleH 6> MTWinEqns   FMicrosoft Office Word Document MSWordDocWord.Document.89q@@@ NormalCJ_HaJmH sH tH DAD Default Paragraph FontViV  Table Normal :V 44 la (k@(No List * Cz>g:z7?tuvw}L`UVDbcde S l m n o p q r s t u v w ' Q R S T U V W X Y  0 ^ & ( ) * + , - . / 0 1 2 3 4 5 6 7 ! W 00000000000000000000000000@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@00000 00 0 0 0 0 0000 00 0e 0e 0e 0e00000000000 00 0w  0w  0w  0w 00000000 00 0Y  0Y  0Y  0Y  0Y  0Y  0Y  0Y  0Y 0000000000000000 00 07  07  07  07 Dbcde S l m r ( ) * + 4 5 6 7 0000 00 0+ 0+ 0+ 0+ 0+000 00 0~ 0~ 0~ 0~X00Z00Z00vX00X00X00Z00X00X00X00Z00T  v  35XprVnp6 N P ::::::::?b$y-;`Mo54*b$*X@6BA<_b$\=}pֲ!%59@8(  P  3 A "`P  3 A "`P  3 A "`B S  ?S ' &  t@ t@Mt@?ELO (*{};?F[]x}2 6 3333333333333336TUWstVq6 Q U V  q-hh^h`o(. 88^8`hH. \ ^ `\o()   ^ `hH.   ^ `hH. xLx^x`LhH. HH^H`hH. ^`hH. L^`LhH.q-  0;       CC/ JkLTs*x,/OrHL@V V oV V  P@UnknownGz Times New Roman5Symbol3& z Arial"qh:&F{& Z    !24 2QHX)?x2 AP CalculusSFSDSFSD