Fonction Reciproque

Question 1

Si f(x) = y alors f^-1 (y) = …

Answer 1

x

Question 2

f(y) = x alors…

Answer 2

f^-1(x) = y

Question 3

f^-1(f(x)) =…

Answer 3

x

Question 4

f(f^-1(x))=

Answer 4

x

Question 5

Comment trouver une fonction inverse ?

Answer 5

1) Écrire y = f(x)
2) Résoudre l’équation pour x en therme de y
3) Pour exprimer f^-1 comme fct de x, interchanger x et y. y = f^-1(x)

Question 6

(f^-1)’(a) =…

Answer 6

1 / f ‘ ( f^-1(a) )

Question 7

Si b > 1 alors…

Answer 7

lim b^x = +- infini

x->+- inf

Question 8

si 0 < b < 1 alors…

Answer 8

lim b^x =0
x -> inf

lim b^x = inf
x -> -inf

Question 9

Définition de e ?

Answer 9

lim (e^h - 1) / h = 1

h ->0

Question 10

(e^x)’ =…

Answer 10

e^x

Question 11

(e^u)’

Answer 11

e^u du/dx

Question 12

lim e^x =…

x-> -inf

Answer 12

0

Question 13

lim e^x =…

x -> inf

Answer 13

Infini

Question 14

log x = y Revient a …

b

Answer 14

b^y = x

Question 15

log (b^x) =…

Answer 15

x

Question 16

b^log(x) = …

Answer 16

x

Question 17

Log x = …

e

Answer 17

Ln(x)

Question 18

ln(x) = y revient à ?

Answer 18

e^y = x

Question 19

ln(e^x) =

Answer 19

x

Question 20

e^ln(x) = x si…?

Answer 20

x>0

Question 21

ln(e) = …

Answer 21

1

Question 22

log x = …

b

Answer 22

ln(x) / ln(b)

Question 23

lim ln(x) = …
x-> inf

Answer 23

Infini

Question 24

lim ln(x) =…
x->0+

Answer 24

-inf

Question 25

ln(x)’ =

Answer 25

1/ x

Question 26

ln(u)’ =

Answer 26

1/ u du/dx

Question 27

( ln g(x) )’=

Answer 27

g’(x) / g(x)

Question 28

sin^-1 x = y revient à …

Answer 28

Sin y = x

Question 29

( sinh^-1 x ) ‘ =

Answer 29

1 / sqrt(1+x^2)

Question 30

(cosh^-1) ‘ =

Answer 30

-1 / sqrt(x^2 -1)

Question 31

(tanh^-1(x))´ =

Answer 31

1 / 1-x^2

Question 32

Sinh x = …

Answer 32

( e^x - e^-x) / 2

Question 33

Cosh x = …

Answer 33

( e^x + e^-x) / 2

Question 34

Tanh x =

Answer 34

Sinh x / cosh x

Question 35

Sinh(x)’ =

Answer 35

Cosh x

Question 36

Cosh(x)’ =

Answer 36

Sinh x

Question 37

Sinh(x)^-1 =

Answer 37

ln(x + sqrt(x^2 +1) ) x R

Question 38

Cosh(x)^-1

Answer 38

ln(x + sqrt(x^2 -1) ) x >= 1

Question 39

Tanh(x)^-1 =

Answer 39

1/2 ln( (1+x) / (1-x) ) -1 < x < 1

Question 40

Quand peut on utiliser Hospital ?

Answer 40

Quand lim f(x) = 0 et lim g(x) = 0
x-> a x-> a

Quand lim f(x) = +-inf et lim g(x) = +- inf
x-> a x-> a

Question 41

Via Hospital ; lim f(x) / g(x) = …

x-> a

Answer 41

lim f’(x) / g’(x)

x-> a

Question 42

f’(c) / g’(c) =…

Answer 42

f(b) - f(a) / g(b) - g(a)

Question 43

Cosh x + sinh x =

Answer 43

e^x

Question 44

Cosh(x)^2 - sinh(x)^2 =

Answer 44

1

Question 45

(( tan x ) ^-1 ) ´

Answer 45

1 / (1 + x^2)

Question 46

(( sin x ) ^-1 ) ´

Answer 46

1 / sqrt( 1 - x^2)

Question 47

(( cos x ) ^-1 ) ´

Answer 47

• 1 / sqrt(1 - x^2)

Question 48

Si lim f(x) = +- inf alors …

x -> a <>

Answer 48

AV en a

Question 49

Si lim f(x) = a alors …

x -> +-inf

Answer 49

AH en a