Demandes associées au chapitre-notebook: "Fonctions- I"

Pour accéder au code relatif à un exemple, double-cliquer sur le triangle du crochet icônique à droite.

Exemple 1

N[((Sqrt[π])/2)]

Exemple 2

(∫_0^∞) Exp[-(x^2)] \[DifferentialD]x

Exemple 3

Plot[Exp[-(x^2)], {x, 0, 4}]

Exemple 4

Solve[(x^2) + x - 3 == 0]

Exemple 5

f[x_] := (x + 1) Exp[(x^2)]

g[x_] := (x + 1) Log[(x^2)] - (1/(x - 2))

x[t_] := 2 Cos[t] - Sin[t - (π/4)]

A[h_] := f[h + x] - f[x]/h

F[x_] := Abs[f[x] - g[x]]

f[x_, y_] := (Sqrt[(x^2) + (y^2)])

A = x[(π/2)] - x[(π/3)]

X = 3 x + 2

foo[x_] := Abs[x (x - 1)] + 1 /; x < 0

foo[x_] := Exp[x] + x Sin[(x^2)] /; x ≥ 0

f1[x_Integer] := If[OddQ[x], 0, (x/2) + 7]

Exemple 6

f[2]

f'[x]

Limit[g[x], x -> 0]

F[t]

f[-1]

f[X]

f[A]

N[%]

f[3, 4]

Exemple 7

f [x_] := 3 x

f [2]

f [x]

g [x] := 3 x

g[2]

g[x]

4 x + g[x]

Exemple 8

f[x_] = Sin [x]

f[2]

N [%]

f'[x]

f[x_] = Sin[x]

Exemple 9

Sum [i,  {i,  1,  3}]

(∑_(i = 1)^5) (i^2)

Exemple 10

Integrate [x Sin [x],  {x,  0,  π}]

(∫_0^π) x Sin[x] \[DifferentialD]x

Exemple 11

{1, 2}

{x, y, z}

Exemple 12

f[x_] := 3 (x^2) Cos[x]

f[x]

f[(π/4)]

N[f[(π/4)]]

f[Table[((k π)/6), {k, 1, 8}]]

f[x_, y_] := a (x^2) + b y x + c (y^2)

f[x_Integer] := x + 1

?f

f[x_] := ((x + 1)/(x - 1))

?f

f[3]

f[(1/3) + (1/2)]

f[1.4]

6.

f[(1/3) + (2/3)]

f[x, y]

a (x^2) + b x y + c (y^2)

f[2, 3]

a = 1; b = -5; c = m;

f[2, 3]

a = m; b = -5 m; c = -3 m;

f[2, 3]

f[1, 2, 3]

f[couleur]

f[x_] := x /; x ≥ 0 && x ≤ 2

f[x_] := (1/x) /; x ≥ -1 && x ≤ 1

?f

f[1]

f[0.5]

Exemple 13

signe[x_] := "+" /; x > 0

signe[x_] := "-" /; x < 0

signe[0] = "+ ou - au choix";

signe[2]

signe[-7.5]

signe[0]

signe[(3/2)]

signe[(Sqrt[2])]

signe[N[(Sqrt[2])]]

signe[π]

signe[tartanpion]

signe[N[tartanpion]]

signe [I]

Exemple 14

f[x_] := (x + 1) Exp[(x^2)]

f[-1]

f[x]

Exemple 15

{M1, A, M3, B, M5} /. {A -> B, B -> A}

RotateLeft[{A, B}]

échanger[{a_, b_}] := {b,  a}

échanger[{3, b}]

échanger[{p, q}]

\(echanger1[a_, b_] := 
\(tampon\  = \ a\); \ a\  = \ b; \ 
    b\  = \ tampon\)

echanger1[a, b]

Clear [A,  a, B,  b,  tampon]

\(echanger2[a_, b_] := 

      \((tampon\  = \ a; \ a\  = \ b; \ b\  = \ tampon; \ 
        Print\ [a, " ", \ \ b, " ", \ \ tampon])\)\)

echanger2[a, b]

Exemple 16

Clear[f, g, x, X, A, B, F, a, b, c, signe, echanger1, echanger2]

Exemple 17

?=

?:=