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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