Fonction Reciproque Flashcards
1
Q
Si f(x) = y alors f^-1 (y) = …
A
x
2
Q
f(y) = x alors…
A
f^-1(x) = y
3
Q
f^-1(f(x)) =…
A
x
4
Q
f(f^-1(x))=
A
x
5
Q
Comment trouver une fonction inverse ?
A
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)
6
Q
(f^-1)’(a) =…
A
1 / f ‘ ( f^-1(a) )
7
Q
Si b > 1 alors…
A
lim b^x = +- infini
x->+- inf
8
Q
si 0 < b < 1 alors…
A
lim b^x =0
x -> inf
lim b^x = inf
x -> -inf
9
Q
Définition de e ?
A
lim (e^h - 1) / h = 1
h ->0
10
Q
(e^x)’ =…
A
e^x
11
Q
(e^u)’
A
e^u du/dx
12
Q
lim e^x =…
x-> -inf
A
0
13
Q
lim e^x =…
x -> inf
A
Infini
14
Q
log x = y Revient a …
b
A
b^y = x
15
Q
log (b^x) =…
A
x
16
Q
b^log(x) = …
A
x
17
Q
Log x = …
e
A
Ln(x)
18
Q
ln(x) = y revient à ?
A
e^y = x
19
Q
ln(e^x) =
A
x
20
Q
e^ln(x) = x si…?
A
x>0
21
Q
ln(e) = …
A
1
22
Q
log x = …
b
A
ln(x) / ln(b)
23
Q
lim ln(x) = … x-> inf
A
Infini
24
Q
lim ln(x) =… x->0+
A
-inf
25
ln(x)’ =
1/ x
26
ln(u)’ =
1/ u du/dx
27
( ln g(x) )’=
g’(x) / g(x)
28
sin^-1 x = y revient à …
Sin y = x
29
( sinh^-1 x ) ‘ =
1 / sqrt(1+x^2)
30
(cosh^-1) ‘ =
-1 / sqrt(x^2 -1)
31
(tanh^-1(x))´ =
1 / 1-x^2
32
Sinh x = …
( e^x - e^-x) / 2
33
Cosh x = …
( e^x + e^-x) / 2
34
Tanh x =
Sinh x / cosh x
35
Sinh(x)’ =
Cosh x
36
Cosh(x)’ =
Sinh x
37
Sinh(x)^-1 =
ln(x + sqrt(x^2 +1) ) x R
38
Cosh(x)^-1
ln(x + sqrt(x^2 -1) ) x >= 1
39
Tanh(x)^-1 =
1/2 ln( (1+x) / (1-x) ) -1 < x < 1
40
Quand peut on utiliser Hospital ?
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
41
Via Hospital ; lim f(x) / g(x) = …
| x-> a
lim f’(x) / g’(x)
| x-> a
42
f’(c) / g’(c) =…
f(b) - f(a) / g(b) - g(a)
43
Cosh x + sinh x =
e^x
44
Cosh(x)^2 - sinh(x)^2 =
1
45
(( tan x ) ^-1 ) ´
1 / (1 + x^2)
46
(( sin x ) ^-1 ) ´
1 / sqrt( 1 - x^2)
47
(( cos x ) ^-1 ) ´
- 1 / sqrt(1 - x^2)
48
Si lim f(x) = +- inf alors …
| x -> a <>
AV en a
49
Si lim f(x) = a alors …
| x -> +-inf
AH en a
