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Homecnrock 7
lona- homogenous 62:
The 4box 2, nae 4-0 coc KP:
ee
Off for “4c
oe:
car)
Zeger ay "44 4 y, 9/7 any = Gx)
Case 7:
WeBog Bf vee
Gtx) (3 @ poynemac
The parkaclar 30:
Setr)= 4a POG ROM aL lof rbe save ata ase)
Aeelace 4-2/0 “JE a2 aer Ae cx
%
ax. Sote BA -¢ Borg = vry ex3
Je Pt Gxt 0x2 16 x7
R= Or 27x 43sx*
=z,
Bat 22° r6 Sx
Evating cof of egval pooers ¢ x ae
(are ésx)-¢0g4 ere 4 35xi)t Ypres 40x 4 sxoi
2r-¥¢ 4¥p-0
65-8 t¥g= = 2410 exp 2x?
co y Je xt
Sguerat $y * Ip
Jb: (At Bx)e™
2
W- 12 $=0
5-8
0-929 4419 206 complementary
eg.
axe
Case 2: Gtx) 1s of th farm Ce) where CR: cork
ch fake 2s a trad cf a function of th sam form
fe (4) fe a
because +e derrvakves of @ are 4
moleples fe &Gase 3° Cex) 1s ather Coos bx or Csmke
Because off the roles for aperenta hing
4he sia aad Cos punch ors oc “sake as
a “1al parhtula- sod a function a
Ye form:
feces fi cas kx + B sin Bx
Case v2 Cex) 13 panned of furctions
te previous 4ypes
Ke rede fe 4vaC 506 fo 2 2. preccac”
YL functions of te samc fype Fer
(pstarce, 2 sotving fhe $F < wave fg:
Le ay/s ty = x cos 3x
fo A= (Bx+ B)cos 3x + COx+h) 812 3x
lax 5: Gtx) 1s a sun of functions of hese /yocs
Ce use be casey varfeek jprrnegole of
sperposchon, hich says i jy, 27K Yo. 2
200. of ay." 1 by" ey = Ccx
“y “+e “4 oy = Bcx)
respectively, L402 gy + (Gog 12 2 S20 Oa
ay"r Sy! 10g = Gtx) 4 Gt)
Yummacy of vadeterrnined —cochl’:
Gex) = | First poy gp
Gxt ¢ Oxt Ix... r4 xt Ao
ak De ax
Ccos kys Coin hx Boos khrt Bio bxSummary of vnade. coc ZL
IX) | “po Cx)
: at
1 Bex) = 8p Kt ay, X°% | X90 Ay x? +Apy, x 4.. ¢ Alo)
4 @o
2 wx s/h, x? at A)e™
2. GG CKJE x (An thy, X t.. tfha)e
3 Bene” sin Bx ALM 24 Py, 2%... Boe
at
ae cos (3x * (By x "+ By, x4.
x
Qm tx)e~ cas [2x At Bes Bx J
n=max Cr, p)
Lote: 8 ys the pwltipaaty of
4. feo iL r20 76 a 100 of He Charachkris Ko
$gvale on,
2 ree ren i$ a rool of the characteristic
epvaleon
3. r= Kt BEHi gher der Kintar Ce.
Table ee
4 _Llang const ) A
2 5x47 Px+8B
3 3x?-2 Bx* +Bxole
y x3- KH Bx2t Brin Car €
5 Sia YX Lica ¢vx7 Bsa¢x
6 COS Ox Bcos vx + B sin vx
7 en fer
& (9x-2) 6 (Ax + B)e™
g xe (Ax te Ber Ce
, oe axe.
70. C0 4X Ae casvx¢ Be™ sia vx
YU Sx? 8/10 YX (Ax*¢ Ber) cosvne (Ex Fee G) sing"
3
12, #O°COS YX (Bx + Be * cas var (Cet Oe si ¢xvw fe nbiy es
ies 2(, ‘ge 429+ Gp
pensoy bye baru ye
pen outy0e op yt (49d
(Gta zs by
% Wp oy
104.7 1Y 47. Wt | pe) 08 ,,219784 1/50, 2 49S. |
fo) tm zt A 2294 0,» UW)? /I 0, 22 + 19/503,,,2 P| 2
ow fo why = food by
7 YO ‘tb
Jeep Ob 1 Ge eae wf
te)2d Used é ie a * goneou fed by ae we
60 Y Udit pve ph r1d 5079 |g
of 2 Jf PF 7 his bp deol
pJ ase +4/s02/),7 79 U8 % tye s02 7 | 7
wed (ut + “4p U+Y), 2 peor Ge DP Wd
7 2d) ©
0=|/ 27 -
$y 0 27 oC
or | eee 12 tbe | porvoclye EP ya Gyd|
yoo! 24¢f¢ Je Aion
spores OF sopmgreid cag)
by 72.9 Lip /0e “t #7 soprqeu: vayt IXPro, bic Lac LE using rhe re FBO
Of ondetermuncel CocfF:
2 YY. be** | @aplementary fanchow
The AUK sod:
qe
ee
Ye comptermentary furckon Js:
feck) = fem
etx) = 2 Ae
etx)? ¥ Ae
2 fe. yhe™ = 8¢**s0
SptX)= Axe *™
Spo'= Ale** rare)
So "= fle gyn fe
ve 40x BEO 9 x EO = ae '*
A=2 Dp (x)= 2X ex
2 Ycx)= cot 4a 4axe™
“2x
| get Ge" Gegt ey tMy = 20°" 4¥K-12
ay r by't cy = Gx)
Cc sod: ?
JE? * Ip 2 4 GeCX)
ay"? by" + cy =O
Jecx)= g2- ty 4 ¥ =e
Py: 22
Lr2fe"r+7Q¢
fe txa= AB +Cxrh
px’: 2ABe "+l
Sa Cx)" +B e
oy = AB 2 -0C2ABe™ + C)+¥(ABe's Cath)
= 20% 4 K-72
per 5 OBe** - Cr tA BE ¢ Ce robe
zx
= 2¢ 4G K-S2
-2x
D> OF 2c"
%Cx=¥ XD Cx
-¥Cr¢h =-712 9 -¥ + whe 12
» yvb-=-8 > \=-2
Sp Ke X -2
-2x
Dy) = ce 4Ge + X-2
xedD Loe ee"
I * Spt ie
Iptx)= g*- 720
Py= Zs
Yp* ce *rge*
Je Ay"t_Bp2 ©
Se ie 2fy + 8B
‘2. 2ff
te
> 2A - (By *+ By 40) ~ ac”
3 A- Ayi- By -C = 8¢
- Ay? - By t2A- C= e*wg y"-y" 4 2%
4 fp? fe
fp= firg*- yore
2 y= t/
=) Ge +Ge
fer hyir By! ely rb = x
’ 23 hy?r 2 By + C
te
2 6hy 12 B
“a: 6B
2 6 + 6hy +2 B -3 Ay*-2 BurC - ty
-GY-b =x
a
-3 Ay By? =2 2 B=
6 Ay - 2 By- Y= x
Ee re
“Ayv7) yoy by 6K o ge BN GEN
Yer (x)= Axis Bute Ce4d
Lp c= 3AxereBX 7O
Spe Gy" = 6Axr 2B
DEN xt 2B -GAK 42 BxAO)-6CA KH Batt Coy D)=
- 6 x24 3x ebx
> 6 Ax 2B -3 Ax? eBx-C-6 Ax? - 6Bx'-6Cx- 6h:
Fo 644 ax bx
> -64+-6 oA
-3A -6B=3~ Bes
6A -1B -6C +69 Cx 3
2B -C- s6hze9 > A=
3 2
Sp x7 KF 7
rt -)
Gor € 2 Lf -0-6
2423 m~ -2
ex
Yy, (WD Get Ge
2, x Zz 3x 2x
Dye OOK - Ft! eGI Sy! =2x > vet- x46
Yo C2 Ake Bx?¢ Crt
yp = 3Ax*+ 2Bx7C
gp": 6Axr 2B
» gAre 2B- sC3Axniee BxreCJ= 2x X*LKes
2 6Axs 2 B- (sAx*- 70 Bx -SC= 2K YK re
2 +15 Ax?+ x Ce A- 708) #2 B- FC 20° KR Kh
~j)-3A = -4) A= Zn
6A-70 Bz Ref
oe + 6y = - 2
2B-5Cz ove 22 x
= 2, 2B x, % v2
= yp 5% x + & x LZ
ow od 2 os
ees sips OFX
7
- a re4
yh Os Gr G-e*
2,3 ,.% BF .
Y= Bx + Fa Bix rOrGe