Toto Eff EEE 'Itoi2019 LI LEHI 71011kt

* I. Ca) f's dx = f !zfExt¥)dx= ( EG - x )

"- 4G - x )

"] ! = - I

(b) log x=t It 'EHI¥ fee-×dw×g×T= f! off = ( 2ft ] !=2(rz - t )

( c ) EET KIEIAIE f ¥*=f¥e ,DX = f. It = log little C = log ( Hex ) t C

# Hoots

(d) Ctanxtl ) ' dxt III: Ctanx - 1)3dx = Sti; I Ltanxthiltanx - 1)3) dx=o

xDg-

# z f ! X dy = fol (s - ry)-

dy = f ! ( g - bryty ) dy = g - ( 4y%) ! + I = Izr×tB⇒EE

.O 4 9

¥3 (a) f- (x ) = It Sinxcosx = It sin 2x > I > o ol EE f E EEN- tot- OT , ( 9¥71- Itt ) OI Fit 7E2HEtet .

(b) X= Htt KHERI E fo'T fix , dx = f! tfitidt = ( tht ) ) ! - fotfltldt = IT

'

- f! ( t t i ) dt = Iz'

- f! theft at =2- it

# 4 (A) 1=1! flxldx = f! # e- Adx = f - Ee

- TX )! = I ⇒ ⇐ z

x -

-E E.EYE o FEME

(b) Efx ) = ↳ xftxsdx-forxe-wdxtfozte-2tdttf.EE/-tjo-fgzte-2tat It nte ! + Spe - stat =L - Ie 't ]? = I

2 01¥

(c) 810101 OFF to -HEHE to 't Jot Gly) dy =P ( Yet ) =P (TX Et ) =P (X Et' ) = f! fix )d× ⇒ GH) = ztflt ' ) = 25 't

it flatfeet .

ze- ' Y

y > oELTZTH 919 ) = {

o YEO

# 5 Y'( t ) = 40 - fo YH ) , Yuk 1000 I ¥7111721122 THIEF HEH -

ddt ( e ylt )) = est Y' ft ) + fo e yet , = e ( y ' Hit # yet , ) = 40 e¥ E 74¥'t tot e yet) = 2000 e to get .

Yw ) = 1000oz ol TOI C= - 10000kt .54-2 thy Yett) = 2000 - 1000 e-

¥00kt .

ytt ) = 1500 E TE E = I = e- 1092 Zz 017¥to Hot THEE t = 50 log 2 ( E ) Iott 'IZQI 0¥01 1.5kg 0kt .

# 6. (a) F YEH : A = (Y f ) E At II 012101 AEI

(b) T A' = AKI 010¥,AZ A' I = A' A' = As -_ I 011 A=AI=AA2=A3= I

(c) T I = det (A- Att At ) = det (( ATI ) At) = det ( ATI ) - det (At ) OKE det (A) = deft At ) to .ELTZTH AE It to#2¥

(d) F HEH : txt toH2¥ A =L - 1) E ATA = (1) = I 017401 det (A) = - I

(e) T det ( XI - B- ' AB ) = det ( B - ' ( AI - A) B) = det ( AI - A ) ol EE FEET ettoothtol Hey ,

# 7 ( a) AEI 076162101 BET C 21-71-2161-01,

B = BI = B ( AC) = ( BA ) c = C 0kt . EEt2tH OF ZEE ¥961- Et .

( b) AB (B - 'A

' ' ) = A (BB " ) A- ' = AA- '

= I 011 (B-' A ' ' ) AB = B-' (A- ' A) B = B-

' B = I OIQZ AB El OF ZEE B- 'A

- ' 0kt .

# 8 det (A) = I,det ((AB ) ' ) = 2

(a) 2 = det ( (ABY) = det (ABAB) = ( del- A)-

( def B)'

= det ( B ' ) : det ( 134=2

(b) ( BA)-

= BABA = A-' ( ABA B) A = ( f 7) ( ? f) ( f f ) = ( Y } )

# 9. (a) det ( RI - A ) = det ( ¥ ) = r

'- trio = ( r - 2) (r - s ) ⇒ ri - 2

,r , ⇒

① res : KI - A) (f) = ( I ) (g) = ta -38 ) -

- (8) ⇒ a- - 2b in -

- fi )

② res : GI - A) ( 81=(77/11)--4973 ) =L: ) ⇒ a- b iv. =L: )

(b) xo -

- G) =L: i ) ⇒ LIKE , it- '

i' f- Eli 's' ) = -344) ice 's.a- I

(c) Xn = Axn - i = A' xn - z= - - - = An Xo = A

" ( Ivi t Vz) = FAV, -1¥ Any = I riv , -1¥ riv , = F- (4) t"

(t )

# to Cal OCP . get on THEH'

Foto#Ef M=( ' IP Ig ) E 12764 Eat. 12-101 (

t - P P ) ( f) = ( t ) 0171oz EIHL'

Efodtot E 0,4ft .

q t - g

Z,101 E'T'M 8oz of- I I

, Eh IE 't ¥9 EH22401 FIE oleo't TOI,EEE EKIKIE to#2¥ It E l - P - of 0kt .

P . 870 Od 171041 Elton E Eff 'd I,I - P - g E ITE F Fit . 54-21- H HELI - E E

,Eff 'd 1

,I - P - G Zz 7- Ect

.

(b) l l - P - 81 El OIEI 101 FAHtot E.Hoh lol I,IFNI E'T Kitt Ehl EITHNE l - P - Gt - I

, Z P -181=271 - Elo - Iof'

Etet .

ocp , get all THE H P tf # 201240¥,post grit ¥4041 101 4-40¥ Ett .

Etta - H 101 EEN E'' I' HIT EM iefot TYEE EINE Mt ( Yf ) off .