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class handouts0001 - ,~ L 9"0;J tAD'1)0=1.~'O'0j;C;j ~:t-p...

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,~ - \''1)0=1.~. "'O"('0 j :;C:; ~ L 9("0-;J tAD ;j- -}-9 ~.~ ..~ -rzr q~ --p t:-«/~ +dJ~ ¥D ~\fUOJ 91 :t j-r "e~6 , ~.7Vy? cr":rX'5";:J (V/:t= !j()O(7/ J ;S: -7- dP' ~ L q 1''07 -+d ~ -f'O ~.t-rpvD ~ t1'\~ "OS ~ \X?d .~ tq,I~Jv·o .~~ g~ j- ~I )( . -r,-~~ 'JJO.J ~~~~ .lL. , JIL1 ~ L 7/= [T- 0 ] - 7 ['(O~7g:OJ -,?;--'/;.)':;]OJ] -
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II .J.1 -b- £:: \ + \ 'e\ [\ I - 0 \ -t ,\ + ~1-7,- f)¥ -lL =1L -'-t.-.-JL ~ 11.) C;o') +\. ~lL)qO) - \ + \-(0) g<S + 1:: U ') YO:)' _. J \ \ \ _'-.LL ' \ \ 0\ . 0L '/9. r-n-..1L) ~O? - \ + . \ \.-:; JL 7 sO")- \ trP ,':}Jt.'J'1-19 's \ -\-\~ '- 7-lL)~\9 Os \ I . ~ ,~ I --,~,,\ ~~ ~I - I L '+ ( \ ...,'0 ~ ~ <::t = 0 = '-.j-LLj UI 9 I \..q f'b] v, \ -;) ~odJ ~~ ~ ~ [CiAo] LAo ~Cl\}-rJ s.~ :t j::T ~~n~
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~ -=t- _. '2.-' h h T = yp ~.-\- £..-'7 + 'l. =r S' <:::> .- J + -e -+ ego:> -:::::- -e p ~ + 'V G( '9 C; ~go7 + G~o/' Ee~\9 ~ _ Q-P \.. 8'Jd9 + '07lA2.\-) e<;QJ ~ ~~I
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Q~ ,,"'xI J o = \)()\f ~CVJ ~ ~~d-o QC} -t~ ~C") "dC") - -nrof"' -y-.o.~UU '. p-oe) -0-'1":) ~J~ ~C"f JO_ () ::=.. ,,'-")(71 t ~cY1 ~j-' +I \. U){7, :.t ';"U)() j _ '--'f x = \~ ~
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~~J--~d J - ou-~:±- ~:::L '?-Il.J -1-. ::::l ! .1- " 1:. 'e ..••. o + ~ J3-56 t 'Z. ':7~ - -::= 'e h ~ == '- T 7 C;; " Qoh-t0 -1'10 o --= S3CS6.\--:=t~- = ~
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0=--:) <1.-=. ::>+ 0 + 0 .::= 0 <:: -:) @ + q~~ + 2..:::t ':)\ -" -= ,,7- 7 <;; 8~-="J <1 =: J -\- ,0)~- =.Qg ~-= -0/)0 56~ + -'7 -::l- =: - oyo- ~r(\ ~i _- I J + 1- '"";(,_. - OJO i I :;pvi ~ - -::: -'5'2.10 > ~ ~rib'::\ ~'f"b 4 I -L -+ \. 1-1<7 [.1L<eI-~] - =. '\>01 I [~ +- 'e]- \- ~~ 1 ) ,~ I i +- 0 =-\..>< J l~: i l , ~ ">(.LL~ ~ r"L '><:J .l!. I ~::fJ t~"?~l1 t -t >("Z5 J' . ~ ~+ 'e -to -z..~ .. l' -;)L.=1. ~0 J =- (x;Q ! '@ ~ '".' . ,. '\.. , ' ,. I
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o ;>JL ~ - h "2- ./ l J V2r 'l< ~ d::= ..l1 q-\-~ . <!.( LL + h )= Pcb -e rv:J CW = JI-ll X. - -1')" - d.- =- W " 't.. ••••• .1l ~ -"2.. > t: -- ~ -'" :::. 4..).. -,..11 'T + ,...A lL - J-'e- d 7..). :::. ""2. -" .11 't + "-\~ 'e =tI ~ ~Q1· 10 ~vcow If c =- .J. Jl. -\-'-\ 'e. -t J.. -e it ~L-? ~ ..J-'e
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L~Jl= '1 ~ - l-,s ~cYI <:1::= .Ctr-~~ ~--vu ~d0/ '""'~ ...~~ 0"> Lfb - S101 =-,,/\ h~ J'O 0= ~ ~ O. i. ,"1 - n-e)~ :: . . "1.. '1\.- ~ Ro\ "::. '- '-'), A. £'1~ - L ~ h.9.::: ~~ - h.9) ""l. ~ -= (~7 (\ ~',-'1 '=-1\ ~i -hE) =0} 01'e+~Q :.~O\ ~~y.(
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IJA.r.y h-\p'" () 1 e...r : (0 1)( i=. -i~i...,. ~ Ve.rll(..~, A.4.., Ih f'''' 0 *t f.,' .~ A~ ~...,.:& 00.." .f(~}-.x. ~.[i::- )(.1 -~ '.. ~t) ol, J,,-.c, A...(' ~ ~ r ".~ t" ~ h 0 r)~ "n"tDo,J ~ ~::. -~ ~::. "\I} ,. e.A:.1 ." c.x Vo 1\4"" eo of box V ';::.L..1-" ~i,... th ~ ~ x. c.." ••.•. tr~J •• 7~ .q. x.,. L .$ 10 8. ~ L.~ 10&-1)( ~ V ~ ~ o~ -~)i:). X. 4 . 4 t ,,'- - - - - " ~ J 2. ~ II 6 - x) :::... 0 )(, c: .... 0'::;>- ,,::.. 0 h1 i " ;"" \( P7 . vol't~(.. ~ ::;t'}08>< -,:z.~=-o •... .,.e.-; r,"eo-I po; ,,1'
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Odd sine-x) = -sin(x) csc(-x) = -csc(x) tan(-x) = -tan(x) cot(-x) = -cot(x) Even cos(-x) = cos(x) sec(-x) = sec(x) ta:1( Q .l- p) = tan! (1) ± tan!p) 1-/+ tan(a)tan(~) sin(n/2 - u) = cos(u) cos(n/2 - u) = sin(u) csc(n/2 - u) = sec(u) sec(n/2 - u) = csc(u) tan(n/2 - u) = cot(u) cot(7t/2 - u) = tan(u) tan(2x)= 2tan(x) 1- tan 2 x Half Angle Identities sin(x/2) ~ t-; cos(x), COS(x/2)~~ tan(x/2) = ± 1 - cos(x) 1 + cos(x) tan(x/2) = sin(x) 1 + cos(x) tan(x/2) = 1 - cos(x) sin(x)
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CO~GEPr Which of the followingexpressions calculates the area of the shaded region? (a) ld f(x) dx - n(J(a))2 - n(J(c))2 C\b) r d f(x)dx _n(f(a))2 _n(f(C))2 ) Jo 2 2 /@r b f(x) dx _ n(f(a))2 _ r d f(x) dx _ n(f(C))2 L vJo 2 Jb' 2 (d) fob f(x) dx - n(J(a)? -l d f(x) dx - n(J(c))2 (e) 42 OO<ity is the derivative of position. A«ele<ation isthe derivative of velocity. Flipping it ~und, velocity is the integral of acceleration and position is the integral of velocity. With that said, Adam the Alien traveled in his sp!'tcecraftwith a velocity of 2 light years V(t) = -3(t - 2) + 12 ---- for 4 seconds. How far did he travel? s Velocity in •• Ll~tYAA[;! Seton<! Here is a mathmatician's solution to how far Adam the Alien traveled. If the solution is correct, select (d) below, otherwise, select the line containing the mistake. (a) Adam traveled the area under the curve, which is (b) 1 4 V(t) dt = fo\ -3(t - 2)2 + 12) dt ~ 32 light years. ~es, the solution is correct.
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-; , What V-substitution would you use for the following indefinite integral? J 4y dy L{ ~~ LL../::: d u. :+- -+ \ V 2 y 2 + 1 __ . ---I .... J (aJ u ~ 4y ~ \ !:."" 1..0::: "-: 'j clYl ~=2y2+1 -J (c) u = J 2 y 2 + 1 ol J':= ~ (d) u = y cl~ j~~l'W ~ ~\ k O\~-t e \ .- C Ir--e.
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