20 pts..Bonjour à tous svp aider moi à faire cet exercice. Merci d'avance !
Questions:
1/Déterminer Df et calculer les limites aux bornes de Df.
2/ Calculer f'(x)
Questions:
1/Déterminer Df et calculer les limites aux bornes de Df.
2/ Calculer f'(x)
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Il y a bcp de fonctions...1) f(x)=x-√(x²+2) ; Df=IR
f'(x)=1-2x/(2√(x²+2))=1-x/√(x²+2)
2) f(x)=2x²-√x ; Df=IR+
f'(x)=4x-1/(2√x)
3) f(x)=(x^4-x²)/(x²+1) ; Df=IR
f'(x)=((4x³-2x)(x²+1)-2x(x^4-x²))/(x²+1)²
=(4x^5+4x³-2x³-2x-2x^5+2x³)/(x²+1)²
=(2x^5+4x³-2x)/(x²+1)²
4) f(x)=x³/(2x-1)² ; Df=IR\{1/2}
f'(x)=(3x²(2x-1)²-x³(8x-4))/(2x-1)^4
=(3x²(2x-1)-4x³)/(2x-1)³
=(2x³-3x²)/(2x-1)³
Lim f(x) = - ∞ Lim f(x) = - ∞
x→ - ∞ x→ +∞
f '(x) = 1 - 1/2 (2 x)/√x² + 2 = 1 - x/√x² + 1
2) f(x) = 2 x² - √x Df = [0 ; + ∞[
Lim f(x) = 0 Lim f(x) = + ∞
x→0 x→ +∞
f '(x) = 4 x - 1/2(√x)
3) f(x) = x⁴ - x²)/x² + 1 Df = R
f '(x) = (4 x³ - 2 x)(x² + 1) - 2 x(x⁴ - x²)]/(x² + 1)²
f '(x) = 4 x⁵ + 4 x³ - 2 x³ - 2 x - 2 x(x⁶ + x⁴ - x⁴ - x²)
= 4 x⁵ + 4 x³ - 2 x - 2 x⁷
f '(x) = - 2 x⁷ + 4 x⁵ + 4 x³ - 2 x)/(x² + 1)²
vous continuez