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~6 6
Z ((I) = Il0 cC7 S ~ t 1- n (t) = A0 Co S LJ~ t + ntt j a
~COSu71 II- S I[o- b-I-a--fo~J S~ce f (t) s a- 1udOn oJ +~
b Rr JI tl) ( t) (efl) ------------------------
=(flo CoS V t t n(~( Ao L05 U~2 rn(bzV
fI zeCos Lv t l ) CCoS U 1 ) f II CaJ (u t) n1
lJ
-+ flo Co S (~tz) nt ll) + n (l) h (tz) ~ --shyo Rn (l-t~)
------
BIL
amiddot Jb j(t) dK = I a
6 2(-L~U-I2)Jr-t2 [-~+- 4~~2gt(J 2shy
= ~ [- + 1t(6)~ IZ(6) + 2_ If(Z)l+ IZ (Z) 1 J2 ~ r3 J
j bc-t)Jx- = 2 [33jJ= I (L
3 [- x1 8x3 ~~J 6~l lJ + - shy
3 2
~ (~)32 3
[r----Lj_]~ =
= Z [-f+- 2~q_ ~X-3J
E[X)
68 01 f(L)K - ~ ba (pound) = L - e (x-K)
(1lt0 bull
()(J
_05~ 0middot5 J( i OS S(x-Jlt) -0middot
lt)middot5 e -05eKr KI 0125 e a
()
F(a)
-1-5~ K -Jb F(Q) = ~ 6Z5e- shy- e- j ( CL-K) 11_1lt K=o KI -5~S
bull -0
e
0 z 3 I0111 0f7 5 )lX- JL--IL X=- i X- -t~51=~2 x - e
1lt=0 XI x-v-Ylbull X= f
~(_l -1 to -J-- ~ ~ ~~ ~ L - e 7C I ~-I)r dt
aI ~
= ~ (I)
-l ~ - 1 J d pound[~] = E[K-((-I) +E[~D
cP ~-z -)A (~) e0 1lt -) K(k- I)
[ [X-(X--I)J = i ((~-I) _ e L ( (X--I) (x--l) I (2 shyX I
~t7 bull oP
()d - 51 l ~ Z t - z - )1 Z e _ 51 ~x 1 - ~CZ
= lL l e 51 ~ - shyd=4 2j I
~ z ~-z) t [~J 5l Z+51 l
~ ~-t- ~ ~ ~ ~gt ff ~6~ EampJ -Z -L
==
= l3 15
P(-SltX(5)= F(5)-FC-5)
~ ( 1-5) _~ ( 12)5 5
~(-)- GLC~)
1- ~L) - G((~)
= I - CDZ ( ( amp) _Glt- ( L2)
= 1- omiddot 2 J2 - O 15
~O-~3 1
G32
1(0) = pc dgth-o) ltOf-lXo) f JCgt~
tJ (U)= P(d- lt- l~o) ~ (1+ l1~o) iL (~
j(l(d) = J~r2 I~gtd Ix-((~ ~ 7ft
~
~ - (K-Jz Z X (K) -= -L e b
fztt (
P ( dgtIl () p ( JL ~ C) = I - P( 7C (x)
= J - F cXo) Q ( )
P ( dlt - Il~) = P(~- ( -~o) ~ Q (Y~)
- - -
B36
o
l ~
P( ( - (L1 J -2~ J J emiddot1 X-z JeJ~ ILl 7 4 4 e X dLshy
-2 _I - z = (~- ~)C2-Z~ )
~ - L PU(xdtJ 4~f) ~ (0058)( I 123) ~ OmiddotOll
------
BIL
amiddot Jb j(t) dK = I a
6 2(-L~U-I2)Jr-t2 [-~+- 4~~2gt(J 2shy
= ~ [- + 1t(6)~ IZ(6) + 2_ If(Z)l+ IZ (Z) 1 J2 ~ r3 J
j bc-t)Jx- = 2 [33jJ= I (L
3 [- x1 8x3 ~~J 6~l lJ + - shy
3 2
~ (~)32 3
[r----Lj_]~ =
= Z [-f+- 2~q_ ~X-3J
E[X)
68 01 f(L)K - ~ ba (pound) = L - e (x-K)
(1lt0 bull
()(J
_05~ 0middot5 J( i OS S(x-Jlt) -0middot
lt)middot5 e -05eKr KI 0125 e a
()
F(a)
-1-5~ K -Jb F(Q) = ~ 6Z5e- shy- e- j ( CL-K) 11_1lt K=o KI -5~S
bull -0
e
0 z 3 I0111 0f7 5 )lX- JL--IL X=- i X- -t~51=~2 x - e
1lt=0 XI x-v-Ylbull X= f
~(_l -1 to -J-- ~ ~ ~~ ~ L - e 7C I ~-I)r dt
aI ~
= ~ (I)
-l ~ - 1 J d pound[~] = E[K-((-I) +E[~D
cP ~-z -)A (~) e0 1lt -) K(k- I)
[ [X-(X--I)J = i ((~-I) _ e L ( (X--I) (x--l) I (2 shyX I
~t7 bull oP
()d - 51 l ~ Z t - z - )1 Z e _ 51 ~x 1 - ~CZ
= lL l e 51 ~ - shyd=4 2j I
~ z ~-z) t [~J 5l Z+51 l
~ ~-t- ~ ~ ~ ~gt ff ~6~ EampJ -Z -L
==
= l3 15
P(-SltX(5)= F(5)-FC-5)
~ ( 1-5) _~ ( 12)5 5
~(-)- GLC~)
1- ~L) - G((~)
= I - CDZ ( ( amp) _Glt- ( L2)
= 1- omiddot 2 J2 - O 15
~O-~3 1
G32
1(0) = pc dgth-o) ltOf-lXo) f JCgt~
tJ (U)= P(d- lt- l~o) ~ (1+ l1~o) iL (~
j(l(d) = J~r2 I~gtd Ix-((~ ~ 7ft
~
~ - (K-Jz Z X (K) -= -L e b
fztt (
P ( dgtIl () p ( JL ~ C) = I - P( 7C (x)
= J - F cXo) Q ( )
P ( dlt - Il~) = P(~- ( -~o) ~ Q (Y~)
- - -
B36
o
l ~
P( ( - (L1 J -2~ J J emiddot1 X-z JeJ~ ILl 7 4 4 e X dLshy
-2 _I - z = (~- ~)C2-Z~ )
~ - L PU(xdtJ 4~f) ~ (0058)( I 123) ~ OmiddotOll
68 01 f(L)K - ~ ba (pound) = L - e (x-K)
(1lt0 bull
()(J
_05~ 0middot5 J( i OS S(x-Jlt) -0middot
lt)middot5 e -05eKr KI 0125 e a
()
F(a)
-1-5~ K -Jb F(Q) = ~ 6Z5e- shy- e- j ( CL-K) 11_1lt K=o KI -5~S
bull -0
e
0 z 3 I0111 0f7 5 )lX- JL--IL X=- i X- -t~51=~2 x - e
1lt=0 XI x-v-Ylbull X= f
~(_l -1 to -J-- ~ ~ ~~ ~ L - e 7C I ~-I)r dt
aI ~
= ~ (I)
-l ~ - 1 J d pound[~] = E[K-((-I) +E[~D
cP ~-z -)A (~) e0 1lt -) K(k- I)
[ [X-(X--I)J = i ((~-I) _ e L ( (X--I) (x--l) I (2 shyX I
~t7 bull oP
()d - 51 l ~ Z t - z - )1 Z e _ 51 ~x 1 - ~CZ
= lL l e 51 ~ - shyd=4 2j I
~ z ~-z) t [~J 5l Z+51 l
~ ~-t- ~ ~ ~ ~gt ff ~6~ EampJ -Z -L
==
= l3 15
P(-SltX(5)= F(5)-FC-5)
~ ( 1-5) _~ ( 12)5 5
~(-)- GLC~)
1- ~L) - G((~)
= I - CDZ ( ( amp) _Glt- ( L2)
= 1- omiddot 2 J2 - O 15
~O-~3 1
G32
1(0) = pc dgth-o) ltOf-lXo) f JCgt~
tJ (U)= P(d- lt- l~o) ~ (1+ l1~o) iL (~
j(l(d) = J~r2 I~gtd Ix-((~ ~ 7ft
~
~ - (K-Jz Z X (K) -= -L e b
fztt (
P ( dgtIl () p ( JL ~ C) = I - P( 7C (x)
= J - F cXo) Q ( )
P ( dlt - Il~) = P(~- ( -~o) ~ Q (Y~)
- - -
B36
o
l ~
P( ( - (L1 J -2~ J J emiddot1 X-z JeJ~ ILl 7 4 4 e X dLshy
-2 _I - z = (~- ~)C2-Z~ )
~ - L PU(xdtJ 4~f) ~ (0058)( I 123) ~ OmiddotOll
= l3 15
P(-SltX(5)= F(5)-FC-5)
~ ( 1-5) _~ ( 12)5 5
~(-)- GLC~)
1- ~L) - G((~)
= I - CDZ ( ( amp) _Glt- ( L2)
= 1- omiddot 2 J2 - O 15
~O-~3 1
G32
1(0) = pc dgth-o) ltOf-lXo) f JCgt~
tJ (U)= P(d- lt- l~o) ~ (1+ l1~o) iL (~
j(l(d) = J~r2 I~gtd Ix-((~ ~ 7ft
~
~ - (K-Jz Z X (K) -= -L e b
fztt (
P ( dgtIl () p ( JL ~ C) = I - P( 7C (x)
= J - F cXo) Q ( )
P ( dlt - Il~) = P(~- ( -~o) ~ Q (Y~)
- - -
B36
o
l ~
P( ( - (L1 J -2~ J J emiddot1 X-z JeJ~ ILl 7 4 4 e X dLshy
-2 _I - z = (~- ~)C2-Z~ )
~ - L PU(xdtJ 4~f) ~ (0058)( I 123) ~ OmiddotOll
G32
1(0) = pc dgth-o) ltOf-lXo) f JCgt~
tJ (U)= P(d- lt- l~o) ~ (1+ l1~o) iL (~
j(l(d) = J~r2 I~gtd Ix-((~ ~ 7ft
~
~ - (K-Jz Z X (K) -= -L e b
fztt (
P ( dgtIl () p ( JL ~ C) = I - P( 7C (x)
= J - F cXo) Q ( )
P ( dlt - Il~) = P(~- ( -~o) ~ Q (Y~)
- - -
B36
o
l ~
P( ( - (L1 J -2~ J J emiddot1 X-z JeJ~ ILl 7 4 4 e X dLshy
-2 _I - z = (~- ~)C2-Z~ )
~ - L PU(xdtJ 4~f) ~ (0058)( I 123) ~ OmiddotOll
- - -
B36
o
l ~
P( ( - (L1 J -2~ J J emiddot1 X-z JeJ~ ILl 7 4 4 e X dLshy
-2 _I - z = (~- ~)C2-Z~ )
~ - L PU(xdtJ 4~f) ~ (0058)( I 123) ~ OmiddotOll