Tổng ôn toán cao cấp

VI 'm AE'

l : tim age ten

'

ha'm ctia phuong ai d ag

z l x , yl = ( a

, x t bey t

y l l U X t be yt Cz )

"huiohg phaip :

Bi : Z '

× , Z'

y

Gidi hi { I' g' . Nghiem via he? diogo oggi la' dividing

Bz : tih A =

2-'

2-"

ay , C =

2-"

yy

Tcu: ctiiim diig Mix ; yo I tih A

D = 132 - AC

- t M let ou ! tin

-M ki my ctai

VD : tim uh

,

tri:

l l Z

, × ; y, = a

3 - 6x' t Ly' - fy - 5

Gidi

•

2-a = 3×2 - 121

•

2-'

y = Hy - 8

{ 2- 'x = O

' ÷ : :

y '

- 2

co' 2 ctiiindug : M 14,21 voi N 10:21

+ A = 2- ''

ax = 6 x - 12

B : 2- '

icy = O

C

Zijy = 4

A = 12 ; B

• D = 132 - HC

=

-48 CO

A- so ;D so M I 4 ; 21 ha'

my thin

-45

+ Tgi Ml O y21

A = - 12 ; B

O ; C = 4

• A = 132

- AC = 48 > O N ko la'

qdctr.ci

✓ TIM HE 2 : tim mix ;

yl thou

{ n'a = ax 2 - b y'

-cry

n

'

y i

day

-ee'

y' t z

131

Hit Pla ;

n'

a

Q la ;yl

u' y

T a co

'

• P'

• Q'

a Ix i

y l

Miu

'

P'

y

Q 'e ton ta.in ( x ; y l

• nlxiyl = /

,! Pla i got de t

ly ! Q ( x ; y l dy

132

Choy soo :

go

O

K

ul x ;y l = ) t lie , ol de t Jit Q ( x i yl dy t C

O

VD Tim n Ix ;y l thou

µ'

x : - ax t 8×3

-Gay t fry'

n'

y = 3 - Joi t 8 a'y - 18yd

ul

-3 ; 01 = 4

C- iai

'

a = - 4x t 8×3

-say t 8say2

Ql x i y l n'

y = 3 - 3×2 ,-8x

-y - 18

y L

T a od :

P '

y lx ;y l

-.

- G x t 16ay

Q'

, I x ;yl = - GR t 16

say

"'

y - Qi ton tap u Cx ; y l

Mu ,

y, =/ ! Pla i got Ck t

ly ! Q Ix ;yl dy t C + Chop x

o

'

-yo = O

u

ca ,

y,

= ) ! P lk i 01 ck t Iott Q la;yl dy t C

= J ! L- Ha t 8×31 de t ) ! 13 -30ft 8kg

-18gal dy t C

=L

-2×21 ! I t 12×41 ! I t 13g IF I - ( big / ! )

+ 14dg- 191 - 16

= - 2nd t 2x " t 3g - 3 a

-by 3 t C

Ta co

'

: n f - 3; 01=4

Viay Me. ;y , = ' '

V A' N HE 3 : Ha

.

. ha'm ciyi cao boring guy

tai Leibnitz 1 my 21

gin' Ix )

Con n un t C '

n u

'

v '

n - t '

t Cfn u

"

, un - 2

g "

" "

131 , bit'

y Kl : la' r 'll e"

- 3

C- iai

f

"

( x) = CIn little "

-3) n t C'm 1×2+11 ' ( ex

-3) n - 1

+ Cfn ( x't t) " ( ex

-31 n - 2

= ( d

'

t l l e

" - 3

- 3

t 40.82420

ex - 3

f 2021 I 31 = 10 t 12126 t 4082420

Coring their iainnho

*

y = sin lax t b l

y ' n' let = an Sin lax th t I

y = cos lax t b l

y 'n' lat = am cos lax t b t MI I

*

at t b

y ln' (x) = an e wit b

* ix in '

=

y :÷i : : ".

talk- 11 . (k

-m)x k - m min' n c K

*

y = 'Mt b

(ax tf / n it

* y = Car t b la

y 'n ' IN = am a la - 11 . I x - in - 11)

VIII DE 4 : cho haim ciri z : z ex ; yl

thou dik voi z ( x ;y l

A

catch him :

+ dz la i b I = 2- '

y la ; b l t

2-'

• F' ( x I =

• F' ly I =

• F' ( z I =

• F'ex) = .

• Fig I =

or F'

f z y I - c

'

, " , lui k l

¥17,

2- '

l z I

Az la ; t) =

VD

F- Ix i

y iz ) = 51×-21323 - 4×1y t 11222 - 3×2y z t

Z 12 ; ll = - 2

• Tink Az 12 ; 11

C-iai'

t d

z 12 ; l l = z '

2-y

'

( 2 ; 11dg

y t 11222

-GayZ t 2

• f- '(yl = - 8 a left 1122 - 3rd z

• F'

iz , I 15 Ix -21322 - 8 x ly tf l - z

-3kg

• F' 1×1 = 22

• F'

ly I = - 104

• F'iz y = 116

'

star

2-'

y kill

-'

jiff,

-ff÷=

-3dg dy

Ving dz kill = II de

Vtf 'M HE 5 : oho him 3 bitiy lx iy i al ia

cho 2 otitis M ; M Tink d-go ha'm a've

j tou' M theo hairy MIT

*

f'a l M l l, tf y' lM t k t

f 'z l M l lez

* I

le, ik , l

, I , THAT = I

* T

y ll 'll = ( f'alMl i f y' lMl i fz' 1141)

d ein

y

'

: I'

, ; as i a

, I Vector d-on m: aia I' ki :

I = ¥y . I'

VD :

y l e

Z th

-x ze Y - t

t za

M l

-3 ; t i -21 i l 'll -2 ; - l; 01

• Tinh : He 1191

ha' hug'

HiT

E la'

hiioig D gli 'll

I'

ki huiohg

-tf IMI

Gidi

t f ' la) = 2x - 2e Z t 2 - z e y - l

J ' ly ) = - e Z +2

- gaze y - l

f ' 121 = - ( 2x

ty ) e -2+2

-x e Y - t

t 42-3

+

f 'a l M i - G

f 'y 1141 = - 7

f 'z ( Ml = - 24

+ If l Mt = - 6 la - 7- l, -24dg

+ MIT'

l l ; - 2 i 2 /

I HIT'

l = 3

i'

-I i Eg title i kill

If

=

-'S

vii.M HE 6 : via chuyin' doing

VI : l icy cat trim 1 At co

'

t 2- L t

v It I =

O E t s 3

at Tinh quag ctuong d trim [ 0 ; 33

b ) Tim pt at s ( t) , bin s 101 = - 5

C-icii

b l U Ctl = s It I '

Ft

D-it u = Tt Lu du : dt

u- = t t 1

seal = I lu2-1l2_Wt2_ zu du

M

= L flu 4 - Lu' t t - Lu' t 2 I du

= L l l n " - Hu' t 3) du )

= 2

( Mft - Ig u ' t 3 u ) t C

= 2 ( FIJI . Eg FF ' t 3 Fit ) t C

t a od s lol = - 5

-13115

s It I =

al d = /d ' I recall at =/ !tllt

ME

= -Id " ult lat t / ! ol t ) at

=L

-I t ' - Es ti' + tri- '

if

I

] I ! t ( Eg Itt 1152 - Eg Itt 11

-+ 6 It tilt

-tyg ] /2 3

= 5 , 273

✓TIM HE'

7 : cho flat bin tug trim la i bI Tik gave

tim tai- ai cai c E la, b I thou

f lol = fave

VI :

flat = - att

• Tits fave

fave

Giani

+

gave =÷a I ! I '" ' de

-Ho

-l ! :rs,

a

1 ! ;÷m a Dai: t

t : Los

t 2 = x t 4

Let It = ok

x = t

4 / ! " t'e÷ a- It = 21%2 It' - 31 It

= 2 L

3

•

fave = Az, I

-201-3452-1 =

-Jtgr

• f lol = g cave I

-ct÷ =

-Jtg O E c e 4

'

c

VIIM.AE 8 : Khai trim Taylor , Maclaurin

soo

\

+f"}"÷ la

-x ol' t t tmall.gr le

-x ol "

t kn

'H' A'N DU'

Lagrange

flat

-yla I t f'Y Ix

-x I t 814dm la

-x I '

+ f"' laol

-Xo ) ) t t o ( x - xc ) m

'HTIN DU '

Peano