Etude de fonctions

f(x) = 3 - 1/(2 - x)

1. Domaine de définition

Dom f =  \\ {2}

x |      5/3      2     
(3 x - 5)/(x - 2) | + 0 - | +

2. Limites et asymptotes

\!\(lim\+\(x\( → \+ < \) 2 \)\) f(x) =  -∞         
\!\(lim\+\(x\( → \+ > \) 2 \)\) f(x) =  ∞         
AV ≡ x =  2
\!\(lim\+\(x →  ∞ \)\) f(x) =  3         
AH ≡ y =  3 à droite
\!\(lim\+\(x →  -∞ \)\) f(x) =  3         
AH ≡ y =  3 à gauche

3. Etude de f'

f'(x) =  -1/(x - 2)^2

x |      2     
-1/(x - 2)^2 | - | -

4. Etude de f\"

f\"(x) = 2/(x - 2)^3

x |      2     
2/(x - 2)^3 | - | +

5. Graphe de f

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Created by Mathematica  (April 2, 2006)
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