MATH

Question 1

lnab

Answer 1

lna + lnb

Question 2

lna^n

Answer 2

nlna

Question 3

ln1/a

Answer 3

-lna

Question 4

ln sqrt a

Answer 4

1/2 lna

Question 5

lou de bernouilli

Answer 5

xi | 0 | 1
pi =P(X=xi) | p | 1-p

Question 6

norme de vecteur u(a b c)

Answer 6

||u|| = sqrt (a^2 + b^2 + c^2)

Question 7

colinearite u(x y z). v(x’ y’ z’)

Answer 7

x/x’ y/y’ z/z’

Question 8

2 plans secants

Answer 8

2 plans sont secants si ses vecteurs normaux sont pas colineaires ou ses vecteurs sont orthogonaux

Question 9

concave

Answer 9

si - et encima de la fonction

Question 10

convexe

Answer 10

si + y debajo de funcion

Question 11

si f’ + et f’ -

Answer 11

f croi f decroi

Question 12

eqt cartesienne

Answer 12

ax + by + cz + d = 0 vecteur normal(a b c)

Question 13

produit scalaire orthogonalite

Answer 13

xx’ + yy’ + zz’ = 0 orthogonal = perpendiculaire sinon paralelle ou confondu

Question 14

nb de combinaison entre e et f

Answer 14

e x f

Question 15

def continuite

Answer 15

somme produit quotien ou composees

Question 16

parties d’un ensemble a n elements

Answer 16

2^n

Question 17

le nombre de groupes de k

Answer 17

n!/(n-k)!

Question 18

esperance

Answer 18

xipi ou np

Question 19

variance

Answer 19

E(x^2) - (E(x))^2 ou np(1-p)

Question 20

y’ = ay +b

Answer 20

Ce^ax -b/a

Question 21

y’ = ay + f

Answer 21

Ce^ax + f0 f0 solution evidente

Question 22

sacar angulos

Answer 22

||u|| x ||v|| x cosU,V = UºV

Question 23

intersection droite et plan

Answer 23

{ x = … + t y =
remplazar en eqt cartesienne
te da coef t
remplazar t

Question 24

projection dans un plan

Answer 24

AB x AC = AB x AH

Question 25

tangante

Answer 25

T = f'(a)(x-a) + f(a)

Question 26

nb d'arrangements possibles dans un ensemble a n elements

Answer 26

n!

Question 27

distance(a:p)

Answer 27

|axa + bya + cza|/ sqrt(a^2 + b^2 + c^2) coord de A et vecteur normal de p

Question 28

avant de deriver

Answer 28

Def intervale et continue

Question 29

avant de systeme

Answer 29

E(t;s) € R^2 tq E(x;y;z) €R^3 tq

Question 30

recuerrence

Answer 30

Vn€N Je pose P(n) Initialisation heredite Je suppose qu'il existe un k € N tq p(k) est vraie conclusion Vn€N

Question 31

limites Unxq^n

Answer 31

lin q>1 +8 lim -1

Question 32

deduir graphiquement

Answer 32

asymptote, convergante

Question 33

derive U/V

Answer 33

U'V - UV'/V^2

Question 34

Chasles

Answer 34

AB = AC + CB

Question 35

primitive UxU'

Answer 35

U^2/2

Question 36

proimitive U'xU^2

Answer 36

U^n+1/n+1

Question 37

derive lnx

Answer 37

1/x

Question 38

primitive 1/x

Answer 38

lnx

Question 39

primitive lnx

Answer 39

xlnx-x

Question 40

derive 1/u

Answer 40

-U'/U^2

Question 41

derive lnU

Answer 41

u'/u

Question 42

derive U^n

Answer 42

nxu'xu^n-1

Question 43

derive sqrtx

Answer 43

1/2sqrtx

Question 44

primitive x^n

Answer 44

x^n+1/n+1

Question 45

derive 1/x

Answer 45

-1/x^2

Question 46

derive x^n

Answer 46

nx^n-1

Question 47

integrales par parties

Answer 47

[uv] - {uv'

Question 48

relation chasles integrales

Answer 48

c^{a + b^{c = b^{a

Question 49

{ kfxdx

Answer 49

k{fxdx

Question 50

{fxdx

Answer 50

[Fx]

Question 51

{ fx + gx dx

Answer 51

{fxdx + { gxdx

Question 52

avant integrales voir

Answer 52

si integral + avant def intervale continue

Question 53

integ + quand

Answer 53

fx +

Question 54

inegalite de la moyenne

Answer 54

m < fx< M {mdx < {fxdx < {Mdx

Question 55

valeur moyenne integrales

Answer 55

U=1/b-a{fxdx

Question 56

E(X+Y)

Answer 56

= EX + EY

Question 57

EkX

Answer 57

kEX

Question 58

VX+Y

Answer 58

VX + VY

Question 59

VkX

Answer 59

k^2VX

Question 60

Inegalite de Bienayme Tchebychev

Answer 60

p(|X-U|>e) < Vx/e^2 U esperance e ecart type

Question 61

inegalite de concentration

Answer 61

p(|Mn-U|>e) < Vx/ne^2 Mn var alea moyenne U esperance e ecart type

Question 62

cos et sin est def sir

Answer 62

-1<1

Question 63

cos^2 + sin^2

Answer 63

1

Question 64

cercle

Answer 64

ft

Question 65

tableau cos sin et x

Answer 65

ft

Question 66

cos-x

Answer 66

cosx pair Ccos symetrique a 0y

Question 67

sin-x

Answer 67

-sinx impaire

Question 68

cospi+x cospi-x cospi/2+x cospi/2 -x

Answer 68

-cosx -cosx -sinx sinx

Question 69

sinpi+x sinpi-x sinpi/2+x sinpi/2 -x

Answer 69

-sinx sinx cosx cosx

Question 70

sinpi+x sinpi-x sinpi/2+x sinpi/2 -x

Question 71

cosa+b

Answer 71

cosacosb -sinasinb

Question 72

sina+b

Answer 72

sinacosb + cosasinb