topic 2-polynomials & partial fractions

8/8/2019 Topic 2-Polynomials & Partial Fractions

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by Kr ]hd MHJ 2060 }ipoj 27 Piaylikofaz # Pfr}ofa Crfj}oilz ‑F z}xpom vxhz}oil oz }dh ilh li} fzehm‛

H7 kf}dz,~,kr,}hd@nkfoa,jik

| 6 | Oc yix colm }doz xzhcxa! JFAA%38+?4:2 206: flm fze cir KIRH

Vxhz}oil 67

Noshl }df} >/8/$6$/:$>:2

−%−%%−≦− J t Bt t F t t cir faa rhfa

sfaxhz ic t! colm }dh sfaxhz ic F! B flm J ,

Vxhz}oil 27

Noshl }df}! cir faa sfaxhz ic t!

J Bt Ft t t t %%%−;%− /2$/2$8322: ! hsfaxf}h F! B

flm J ,

Vxhz}oil :7

Mosomh 6:22:

−%− t t t by 62

%% t t ! htprhzzoln }dh rhzxa} ol }dh

cirk mosomhlm ; mosozir t vxi}ohl} % rhkfolmhr,

Vxhz}oil =7

$f/ Noshl }df}

$ /$ /$ / $ / M tJ t t B Ft t t t %−%%−%≦−−% 626=3:22: cir faa

sfaxhz ic t! colm }dh sfaxhz ic F! B! J flm M, Dhljh mhmxjh }dh

rhkfolmhr ~dhl =3:22:

−−% t t t oz mosomhm by 22

−% t t ,

$b/ ]dh rhkfolmhr ~dhl =>22:

%−− lt tkt oz mosomhm by 2− t ozcixr }okhz }dh rhkfolmhr ~dhl o} oz mosomhm by t % 6, Colm }dh sfaxh

ic lk −= , Noshl cxr}dhr }df} 6− t oz f cfj}ir ic }dh piaylikofa!

colm }dh sfaxh ic k flm ic l,

Vxhz}oil 87

Noshl }df} VPtj t t t t t t %%−%−≦%−− //$:/$2$63=:2: ! colm

}dh sfaxhz ic P! V flm j,

Vxhz}oil 37

]dh rhkfolmhr ~dhl t2

% pt %6: oz mosomhm by 2− t oz }~ojh }dhrhkfolmhr ~dhl mosomhm by t % 2, Colm }dh sfaxh ic p,

Vxhz}oil >7

]dh cxlj}oil c oz mhcolhm by 366/$2:

%−%; tbtft t c ! ~dhrh f flm b

frh jilz}fl}z, O} oz noshl }df} 62/2$ −; c flm }df} ~dhl c $ t/ oz mosomhm

by $ t % 6/ }dh rhkfolmhr oz 62, Colm }dh sfaxhz ic f flm b,

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| 2 | Oc yix colm }doz xzhcxa! JFAA%38+?4:2 206: flm fze cir KIRH

Vxhz}oil 47

Noshl }df} B Ft tV t t t t t %%%−;%−− /$/2/$:$222:=2: ! cir faa

sfaxhz ic t! ~dhrh V$ t/ oz f piaylikofa! colm }dh sfaxh ic F flm B,

Vxhz}oil ?7

Noshl }df} =::/$=

%−; t t tP flm =2/$2:%−; t t tV ,

$o/ Colm }dh rhkfolmhrz ~dhl hfjd piaylikofa oz mosomhm by /6$ − t ,

$oo/ Dhljh mhmxjh }dh rhkfolmhr ~dhl /$/$ tV tP % oz mosomhm by

6− t ,

Vxhz}oil 607

]dh htprhzzoil b tft t %−% 8=2: ahfshz rhkfolmhrz ic 4− flm 60

~dhl mosomhm by 2 t % : flm :− t rhzphj}oshay, Jfajxaf}h }dh sfaxh ic f

flm ic b,

Vxhz}oil 667

]dh htprhzzoil b tft t %−% 2?22: dfz f cfj}ir 6− t flm ahfshz f

rhkfolmhr ic 30 ~dhl mosomhm by t % 2, Colm }dh sfaxh ic f flm ic b,

Vxhz}oil 627

]dh piaylikofa k t t t t c %−%; 663/$2: oz mosozobah by :2

2−− t t ,

Colm }dh sfaxh ic k,

Vxhz}oil 6:7

]dh htprhzzoil bft t t %%−2: dfz f cfj}ir t % 6 flm ahfshz f

rhkfolmhr ic 24 ~dhl mosomhm by :− t , Colm }dh sfaxh ic f flm b,

Vxhz}oil 6=7

Noshl }df} p t t t t c %−%; 82/$2: flm }df} t % 6 oz f cfj}ir ic c $ t/!

$f/ colm }dh sfaxh ic p,$b/ Dhljh ziash }dh hvxf}oil c $ t/ ; 0,

Vxhz}oil 687

Noshl }df} :22

−− t t oz f cfj}ir ic }dh htprhzzoil 46:=

−%% vt pt t !

$f/ colm }dh sfaxhz ic p flm v,

$b/ Dhljh! colm }dh rhkfolmhr ~dhl 46:=

−%% vt pt t oz mosomhm by

2− t ,









| : | Oc yix colm }doz xzhcxa! JFAA%38+?4:2 206: flm fze cir KIRH

Vxhz}oil 637

$f/ Zdi~ }df} 6− t oz f cfj}ir ic 4282:

−%% t t t ,

$b/ Cfj}irozh 428 2: −%% t t t jikpah}hay,$j/ Dhljh! ziash 04=204

2:;−%% y y y ,

Vxhz}oil 6>7

Ziash }dh jxboj hvxf}oil 0882:

;−−% t t t ,

Vxhz}oil 647

]dh jxboj piaylikolfa c $ t/ oz zxjd }df} }dh jihccojohl} ic t: oz 2 flm }dh

rii}z ic }dh hvxf}oil c $ t/ ; 0 frh 6− ! 2 flm e, Noshl }df} c $ t/ dfz f

rhkfolmhr ic 63 ~dhl mosomhm by

:− t ! colm

$f/ }dh sfaxh ic e!$b/ }dh rhkfolmhr ~dhl c $ t/ oz mosomhm by t % :,

Vxhz}oil 6?7

$f/ Ziash }dh jxboj hvxf}oil 02822:

;%−% t t t ,

$b/ Dhljh! ziash }dh hvxf}oil 0>8/6$/6$22:

;%−−%− y y y ,

Vxhz}oil 207

Ziash }dh ciaai~oln jxboj hvxf}oil! nosoln yixr ziax}oilz }i 2 mhjokfa

pafjhz ~dhrh lhjhzzfry,

0366?2:

;%%− t t t

Vxhz}oil 267

Htprhzz2

2

/2/$8$

:=

%−

%%

t t

t tol pfr}ofa crfj}oilz,

Vxhz}oil 227

Htprhzz t t

t

%

−

2

2

2

>:ol pfr}ofa crfj}oilz,

Vxhz}oil 2:7

Htprhzz t t t

t==

=2:%%

− ol pfr}ofa crfj}oilz,









| = | Oc yix colm }doz xzhcxa! JFAA%38+?4:2 206: flm fze cir KIRH

Vxhz}oil 2=7

Htprhzz/6/$2$

:22

2

2

%−

%%

t t

t tol pfr}ofa crfj}oilz,

Vxhz}oil 287

Htprhzz t t t

t t

?3

?6?22:

2

%%

%%ol pfr}ofa crfj}oilz,





topic 2-polynomials & partial fractions

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