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0% found this document useful (0 votes)
62 views41 pagesOde NOTES
The document appears to be a collection of mathematical equations and concepts, primarily focusing on functions and their properties. It includes references to various mathematical terms and operations, but the text is fragmented and lacks coherent structure. Overall, it seems to cover topics related to calculus and algebra without providing clear explanations or context.
Uploaded by
patilprahlad16Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF or read online on Scribd
/ 41
a / “VAR AY
+ Lneea -clifteven Mal Equasions of
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Oiset 3
The gemexal \feneor
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00 teen “be tanta nena ce
=n Fis
(4 Pp" ae wt Pa) Y =
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= 5
wh. cpemertcal olution of eof 09 7
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A _dietetenetat eof of ane fermi
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tr fw
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ol I we +
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aw 7
ey 4s eo" + @ary! + sany = RO-
= obtain ce > 6/41 *o¥s +043
=) ind w= |v Ya 4
yl ysl yal
a Taos? i
e +. 4s i
it
Yece+Pz
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ne CE = Clos X + (2 Sine
let y= wsey Y= sin & RIX) = Coser ©
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yl! | Jasin. SX |
Uy = - (YR) de
J.
__= = _(sinx-tosee x ox
i A L
Mo = [ YR) da is L *
oe ;
= | tosx-tosee dx
a enna
rte wos) (de
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Ce ee
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2 .
= tia = [| YR) de —
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7 = + a]
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TI
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t
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aa Zz,
—~
L rr
L 4
1 ela. cosn Fon. |
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L O - WS sina
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Ms 4 2
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w
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asf sae esta} comes ot Lal
1605 3x (La os, 4
rd femsu sda
-2013) +— = cot x)
+ (dau — Hida!) Ru on
= osee 2
pa = muy, t Mae tsi —§
. px zdm Tose x — ot x) OOS Tn (atx). sn
yece sre ts
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ht } |
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corey
Oe ate. end tamte
ef ElaEre TEIN
sthe: ea it) =
Seduted “te [imean’ chite enen tial
flea” pn? romsiient
15 +he fh
be Solved by Maes methods — oliscusseal _
ee tects Qarslier —_{ 1
= —> 2 Stubs titudine, oe
——__Il arn 4 pe.
=) By puring 7 se” we
_Xdy = Oy
aK
[ lt Arata) Spear
eat i
x2 dy = ptnadtn-2
ae
a7 a7Y = otnapt-2) caonaiy
ext
Coetticients patthiy
cependent Varfcibie , titiel com 2 va 0 -——
fe
|
= n(x ec ce
(may-s0) Jem-2013)
Pu ase) 22 ina.
“the _¢ive 2” seduced +¢
XN
a
=
4
q
(Dt0-1) 10-2) 4 2 OCD 42) y = 1 ce +e)
aia pean cierto
4
4 The Ae. fs o-0+2 20
Sin’-a0-20 p2042 =0
~ Olon)=2p (oH +214) 20
(pi (0-2 +29 20
& pionte=0
6 OQ =1th
Ze (entose tcgsinz)- —__y = od
swf ye any eI] :
z ao : |
Z =
LPL =m Se +2767 ~
The 98: fes i yece rez a)
ooo
= ea {.
YE Ce 4 o* (cgtosz + Cgsinz) +5e 422 er
eerie aim 1 5 z
“Ys ty) + 0 [ty i0' (4a) +(g si (4m 4) + 5x
z ==
a2 kms.
—
Yoo =) ameb gly 20.
a)
i ar
(04) -30 rH) y = 0 r
2 (B= -s0t9y = [
2 (9 =40 +44 =e
=> The AF. fs 5 D=4AD th =0
4 (p=2y%=
fp=2 42) 3am
DB xy" 429" 20 Pr =O
pip-yty
=> D201)
1 C04 fg bn)
The gs is 5 4 =tF Pr
aE 2,22
ye (CtozIe +b
ut z =dnat
= Gee A VASA VA AX VAY
“ef nalaes inewx equation go 2
eg _ re cere suet an
The ef of them!” exder fs of the
Qo lars IY 4 atari gy 4. +
as aa” ax
m=) Cax+b) AY + any = Rix) ———)
| ax a —
Phere” Ao, 41 ~-7¢4y ose costae,
The ef” 01) can
| Ninens oltre soot" cofth » comatamt z
oekeicfents | 4 i. eee
CO\ich com eastlsy be Solved.
= BY _purting ort =e in U) me get,
Cax+pdy =aoy
reg
Caxtey dy = a*pto-ny
i _ a7 &
TT Sag 3
0x toy d°¥ = a Dto-.N-294
| ax3
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U air iad
—) Hem cbtet. eu” Com fly be.
lemie the aoe
| sow ~~ — = —
Ek Solve the Pcllowhra olisg, on
8) cot * oly per dY +4 = A cos [ley C1429
ee dat rca 7
ma
er xtize™ 9 ze dma)
The given ea” seshired tos .
Sotto turo gids = 4005 2 Hee aot)
ie : 2 o=ti
—— Teil Qa 0 7 (ontanga) #adnci si =
+ tas (i “silent
a Ge 5 (igetxt) ee
aera cer spate e-3
are)
3
2(ap—4e -ap-2)y = 3Ce%=3)
2 (ap-¢p -i2)y = ae 49
b Th @-£. fs,
4p gp -12 =O
2 WO'= 20 +4p 1220
“HD (D-3) +4 (10-39 =0
S(D=3) (AD +49 =O
- 023 ,-)
oz
u 2
AD 8D 1 4p-8D-12
sai) #9. Ger tsd
Ta) (ap.
z az =
YB Ore lta gh
fp. é i
Mati 2 ton (poeta) fh oata- ee
+ fo UbenGertone tit Co aa tan, 3
Data 16 a
+ 2 Ys taxtay+ GH ax a9 43.
arse 6 y
a
3
Citarts) +10, ax +3
aura Sb nn STA
[> :
MRO) a5 pex toe Hewoing
1) Roy 2 e9% [Spa aek®
whe fesx of Yo
S2 "R00 esincy og cosoxl Yee psinag apie ag
2D R4 = oT Prerta [Y= A Prax 4or40
4D RUD = ars by Yo = At ax +
| SD) Rw) = axa, Mp = AX ty al
t £) Rind 2c Yo = &
SDR =e" simnx of |1 up = 0 (acmta au 05 b1)
08% os bor 2 a
9) lletay = ye Ye = CAanae e
8) [Ring = 29%
de
a
Catpxtuds
10) Qiwd= x ohn ax
Jp = (A+R) shox +Cc+pi) san
eg Il eins = a Ye = Act* -
ROIs e736 Ye = Ae Tape
RAI = tos ay Moz Asin 32 + Rtas 3%.
BOONE
when functor)
sppeamny Fey
Be Ute also present
Pesicwer +,
ny i eo ot
tena 4 Solve the toltnwiny lite. eo using the
J
~ amettod ot Umdebetmineal. Coetticiem ts
——— ee
1) y" suy = sin ax
The ae fs, oH
ry
= Ce = C,U0s aoe Cp. 8h Ba __—
. Asin 8% +B cos 94 —___—_—
= 20cog3x — 38 sinda —_—__—
= -4A singx = 1309 3%
cin gx = 98 60S 3:
a + upshnax $4 cos 3b
= 2 sau —
_ ei) ate WASF BMAF
+
43 aE
=e
Wc=0 = c=0
2BtID a4 <5) gyap ay ~
3
= 1) = 10
3
= 92 10,
iF
@ Yy"+ay = owsax geen Ue = C) tos 3 + ta SPO 3K
Up = xcasinas 40534) + C4 4P
Up = Axsinax 4 xcos 32
up = Altos 34 — BAC 811 3 4 BS
ri
yp = —aAsinix = Asin im = IAx (os 320+ aAcos 2
+ 3G (n5 3% =
Ud