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MATH 122L (3)
Final

MATH 122L Final: Math 122L Notes
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Department
Mathematics
Course
MATH 122L
Professor
Sarah Schott
Semester
Fall

Description
1AHρ圠, 8R45.*.ll b.,m | Review of AP AB Diffinerdiaton eveW_0 -cate一止一change = f (b)-fla) .Endndnneous node of changes N(x) E" ( E-1(x) )·器-f-le) ) . Linene-approx s tanged b fW-痂3xstx:0 hed-dr ーーーーーe9--th -AJu3x at -1.03 ーーー ーーー enth_CTh rnderestimates f(x) near x- CN (x-a ) :Lind-def; la M ineJ! 二 hL点 tal u«L三allex) , Ier a fund or-be continvess-ac FW- t fe) : Fla) 읊 functon fon lat 130 t.... fmtten fen rght H/A asynehies can . IMA describe long term has-to-l level out total distance traveled)三JaLI s (t) I d 1AHρ 圠 , 8R45 . * . ll b . , m | Review of AP AB Diffinerdiaton eveW_0 - cate 一 止 一 change = f ( b ) -fla ) .Endndnneous node of changes N ( x ) E " ( E - 1 ( x ) ) · 器 -f - le ) ) . Linene - approx s tanged b fW- 痂 3xstx : 0 hed - dr ーーーーー e9 -- th -AJu3x at -1.03 ーーー ーーー enth_CTh rnderestimates f ( x ) near x- CN ( x - a ) : Lind - def ; la M ineJ ! 二 hL 点 tal u « L 三 allex ) , Ier a fund or - be continvess - ac FW- t fe ) : Fla ) 읊 functon fon lat 130 t .... fmtten fen rght H / A asynehies can . IMA describe long term has - to - l level out total distance traveled ) 三 JaLI s ( t ) I dReview of AB leges A tient If o co t s If O InX O NOT USE QUOTTENT RULE FOR LIHOPTTALS Review of AB leges A tient If o co t s If O InX O NOT USE QUOTTENT RULE FOR LIHOPTTALSSums m On A f to f high 1 fla 2 (at A k Ax MMA Sum Left-hank anh right knnh swns erect for constants Mch HS dawn f and underst mps Cove up. concave. Down Mnctrons c- Tent ant Sums m On A f to f high 1 fla 2 (at A k Ax MMA Sum Left-hank anh right knnh swns erect for constants Mch HS dawn f and underst mps Cove up. concave. Down Mnctrons c- Tent antAnn Sums It Riemann Sums and elinite On If us re RA Ann Suns tits kno defi RHS Ann Sums It Riemann Sums and elinite On If us re RA Ann Suns tits kno defi RHS3 N- N RA a 2 N -N more innite -ntegral Aon With n su intervals 27 6.79 C property t) dt 3 N- N RA a 2 N -N more innite -ntegral Aon With n su intervals 27 6.79 C property t) dtLet f different FTC Let f ronin vous M t)dt th S Maximum 0, S O S Let f different FTC Let f ronin vous M t)dt th S Maximum 0, S O Seven one f (x) Part 21 f F Ant Ch t at JIN sect dt u- substitution Ch JT f f s X th x C UOUS even one f (x) Part 21 f F Ant Ch t at JIN sect dt u- substitution Ch JT f f s X th x C UOUSList .P.uaf Defini dv h X lxtc. t C Use trick sin x a l- cos L2x) Jx x C ton 2x C List .P.uaf Defini dv h X lxtc. t C Use trick sin x a l- cos L2x) Jx x C ton 2x Cmethod top them Gisser, have h X-2 A (2 2) B C xa 2 3 5 B 12) (32) 2) A (-2) (2. C 3x-5 +0x -3 3x-S 3x -5 xt 2 2 In 2-0 X-2 A A method top them Gisser, have h X-2 A (2 2) B C xa 2 3 5 B 12) (32) 2) A (-2) (2. C 3x-5 +0x -3 3x-S 3x -5 xt 2 2 In 2-0 X-2 A AA (ital t8U-- Improper Integon|s ecesn't fake-inten always-pasitin botーーー ー上ー190 ーflhx when oepel the area an ichapel th ーーーーー be ushovid/be able to Piek anyt His hasn't work w/b A ( ital t8U -- Improper Integon | s ecesn't fake - inten always - pasitin bot ーーー ー 上 ー 190 ー flhx when oepel the area an ichapel th ーーーーー be ushovid / be able to Piek anyt His has n't work w / b는上LTHeぅーーーーーーーーーーーーーー NOTES ER flalde exists for every rivmhe tent then -Re),de-exits-tor-every nunker t 21, the ヒーAL一faLL.li4, b f(x) dk provided the lint. bh- 2lone止421ーーーーーーTAーAvrgesー率_veges * arehox ben).tJ. Lyふd ? ーーーーーーT 氝ーーーーー |probabilit 3 impotant -enhabil-ly function (IP) iser finctonuttihassmoottomrs basic occurences birations of adcomes PLovhomesー Exee Roll a 63idd de t Ravn is 11) -2- -ex- poll a 6-sidel diet-i PLA)-P(B) parkin Mariables-takes oJhemes and gives them numbers Expi Elio 3 Coins rule set $10 Tm 는 上 LTHe ぅ ー ー ー ー ー ー ー ー ー ー ー ー ー ー NOTES ER flalde exists for every rivmhe tent then -Re ) , de - exits - tor - every nunker t 21 , the ヒー AL 一 faLL.li4 , b f ( x ) dk provided the lint . bh- 2lone 止 421 ーーーーーー TA ー Avrges ー 率 _veges * arehox ben ) .tJ . Ly ふ d ? ーーーーーー T 氝 ーーーーー | probabilit 3 impotant -enhabil - ly function ( IP ) iser finctonuttihassmoottomrs basic occurences birations of adcomes PLovhomes ー Exee Roll a 63idd de t Ravn is 11 ) -2- -ex - poll a 6 - sidel diet - i PLA ) -P ( B ) parkin Mariables - takes oJhemes and gives them numbers Expi Elio 3 Coins rule set $ 10 TmExpected value Exp 3 flip 3 far erins FX PC TTT) (a) -2.0 2.0 3 P(H) 3 Exe Flip unfair coin mttric Series Hails taib) how Sequences and S t (A) Write the fat 5-tcrms eries -sum ounces 0-C) Expected value Exp 3 flip 3 far erins FX PC TTT) (a) -2.0 2.0 3 P(H) 3 Exe Flip unfair coin mttric Series Hails taib) how Sequences and S t (A) Write the fat 5-tcrms eries -sum ounces 0-C)FnL5 s,三一乏ー4 - silantean-6-各ー吾anEy-ーーーーーー must be zero lin na e doesn't eenetr vt be hit N is nat Zen lal.)-In(ntl): l ーーーーーーーーーーーーーーーーーーmelt-tethーーーー N+1 lin A-L if Ley If lm flx)al -and-f Hon-lin-Anal ーーーーーーーーーーーーーーーーー,an三一m lm ーーーーーーーーーーーーーーーーーーーーー 느 and d:v, he all dHer r-valves ZE_a_-anti-foran-nal t ris-decreas is monotone if it is either rr bw5f8WoL FnL5 s , 三 一 乏 ー 4 - silantean - 6- 各 ー 吾 anEy- ーーーーーー must be zero lin na e does n't eenetr vt be hit N is nat Zen lal . ) - In ( ntl ) : l ー ー ー ー ー ー ー ー ー ー ー ー ー ー ー ー ー ー melt - teth ーーーー N + 1 lin A - L if Ley If lm flx ) al - and - f Hon - lin - Anal ー ー ー ー ー ー ー ー ー ー ー ー ー ー ー ー ー , an 三 一 m lm ー ー ー ー ー ー ー ー ー ー ー ー ー ー ー ー ー ー ー ー ー 느 and d : v , he all dHer r - valves ZE_a_ - anti - foran - nal t ris - decreas is monotone if it is either rr bw5f8WoL: bounded above IF Hers is nvaler m-t-are M , bended-telone-ーーーーーーーーーーーーーーnstnn点m--------- ndel above and beLu.then ar is A banded louded 빅 wt TEーーーーーーーーーーーーー literal-est 1x-f,-귀 dx--X-I-1 elf power +1 >0 → integral DAE over t 1:0 -d-interal,0Ne ーーーーーーーーーー 0 integrale atーーーーーーーーー "if -pt1 >0 之interal (lit pel L0 ぅint, converges. → p> conver t harmonic series ーーーーーーーーーーーー Has on ths e Lettee -a ontinuous edscossma-fund on-anELol and : bounded above IF Hers is nvaler m - t - are M , bended - telone- ー ー ー ー ー ー ー ー ー ー ー ー ー ー nstnn 点 m --------- ndel above and beLu.then ar is A banded louded 빅 wt TE ー ー ー ー ー ー ー ー ー ー ー ー ー literal - est 1x - f , - 귀 dx -- X - I - 1 elf power +1 > 0 → integral DAE over t 1 : 0 -d - interal , 0Ne ー ー ー ー ー ー ー ー ー ー 0 integrale at ー ー ー ー ー ー ー ー ー " if - pt1 > 0 之 interal ( lit pel L0 ぅ int , converges . → p > conver t harmonic series ー ー ー ー ー ー ー ー ー ー ー ー Has on ths e Lettee -a ontinuous edscossma - fund on - anELol andEX. Z test series conveges for p to had shifto all retumles from eft by one VN N+I flu Oanson RS om a. If an Converges t is 6 n s Converes CT EX. Z test series conveges for p to had shifto all retumles from eft by one VN N+I flu Oanson RS om a. If an Converges t is 6 n s Converes CTーーーーーーー2 we knew en lominedes over-2 So ampm ah_c -220-X Sa lweto use thi Limit Gwpanton lest aitamperisan Test at -sーーーーいーーーーーーーーーーーーーーーーーー 2hーーーーーーーーーーーーー20 an2 04(200 then both,-very or dive LL so becaus e we knov en converg -convenesナ-se-does-esa this-diverge we hng-this- converge romparisan tst EX. Limit Comparlan Test n/ mtCornionnan dominah 교 ae know y, disreges.bc p 느1 en en ⅔ nブーーーー(n24=3) hap_taN교 ast bar which 's So multiply to-anTottomT7 n73 lim 4tn ly--を一一 h has aln) kesn't maHer be dean only k 1 So Co nears -be be-pal !! the you ーーーーーーー 2 we knew en lominedes over - 2 So ampm ah_c -220 - X Sa lweto use thi Limit Gwpanton lest aitamperisan Test at -s ーーーー い ー ー ー ー ー ー ー ー ー ー ー ー ー ー ー ー ー ー 2h ー ー ー ー ー ー ー ー ー ー ー ー ー 20 an2 04 ( 200 then both , -very or dive LL so becaus e we knov en converg - convenes ナ -se - does - esa this - diverge we hng - this - converge romparisan tst EX . Limit Comparlan Test n / mtCornionnan dominah 교 ae know y , disreges.bc p 느 1 en en ⅔ n ブーーーー ( n24 = 3 ) hap_taN 교 ast bar which ' s So multiply to - anTottomT7 n73 lim 4tn ly-- を 一 一 h has aln ) kesn't maHer be dean only k 1 So Co nears - be be - pal !! the youIf previous esantle excep L, C. T 0 er thank L.c. t afte Inlo) Loth If previous esantle excep L, C. T 0 er thank L.c. t afte Inlo) Lothrnating Se
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