📚 Limites et Continuité
Cours de soutien — 2ème Bac
Prof : SOUNI MOHAMED
📍 KHENIFRA
📱 Tel / WhatsApp : 06.76.43.35.51
▶️ Chaîne YouTube : SOUNIMATH
Prof : SOUNI MOHAMED
📍 KHENIFRA
📱 Tel / WhatsApp : 06.76.43.35.51
▶️ Chaîne YouTube : SOUNIMATH
Exercice 1
⭐ ⭐
avec solution
Calculer les limites :
\(
\displaystyle
\lim_{x\rightarrow+\infty}(-3x^4+15)
\qquad
\lim_{x\rightarrow-\infty}
\left(-\frac{x^4}{5}+14\right)
\)
\(
\displaystyle
\lim_{x\rightarrow+\infty}
(-4x^3+5x+17)
\qquad
\lim_{x\rightarrow+\infty}
\frac{x^3+4x}{x-x^3}
\)
\(
\displaystyle
\lim_{x\rightarrow-\infty}
\frac{x^4+x}{x-5x^2}
\qquad
\lim_{x\rightarrow-\infty}
\frac{\sqrt{2}x^3+4x}{(x-4)^7}
\)
Exercice 2
⭐ ⭐
avec solution
Calculer les limites :
\(
\displaystyle
\lim_{x\rightarrow2}
\frac{x^2+x-6}{x^3-8}
\qquad
\lim_{x\rightarrow1}
\frac{x^3+x^2-2}{x^2+5x-6}
\)
\(
\displaystyle
\lim_{x\rightarrow2}
\frac{x^3-6x^2+11x-6}{x-2}
\qquad
\lim_{x\rightarrow2}
\frac{\sqrt{x+7}-3}{x-2}
\)
\(
\displaystyle
\lim_{x\rightarrow1}
\frac{\sqrt{x^2+3x}-2}{x-1}
\qquad
\lim_{x\rightarrow0}
\frac{\sqrt{x+1}-\sqrt{1-x}}
{x-\sqrt{x}}
\)
\(
\displaystyle
\lim_{x\rightarrow1}
\frac{
\sqrt{x^2+x+2}-\sqrt{2x+2}
}{
\sqrt{3x+1}-2
}
\)
\(
\displaystyle
\lim_{x\rightarrow2}
\frac{
\sqrt{2x}+\sqrt{4x+1}-5
}{x-2}
\)
\(
\displaystyle
\lim_{x\rightarrow3}
\frac{
\sqrt{x+1}-x^2+x+4
}{x-3}
\)
\(
\displaystyle
\lim_{x\rightarrow1}
\frac{x+\sqrt{x}-2}{x^2+x-2}
\)
Exercice 3
⭐ ⭐
avec solution
Calculer les limites :
\(
\displaystyle
\lim_{x\rightarrow2^+}
\frac{x+7}{x-2}
\qquad
\lim_{x\rightarrow1^+}
\frac{x^2+5}{1-x}
\)
\(
\displaystyle
\lim_{x\rightarrow2^+}
\frac{x+7}{x^2-4}
\qquad
\lim_{x\rightarrow3^+}
\frac{x+4}{x^2+x-12}
\)
\(
\displaystyle
\lim_{x\rightarrow0^+}
\left(
\frac{1}{x}
-
\frac{3+x}{x^3}
\right)
\)
\(
\displaystyle
\lim_{x\rightarrow4^+}
\frac{
\sqrt{x+12}-\sqrt{3x-4}
}{
x^2-8x+16
}
\)
\(
\displaystyle
\lim_{x\rightarrow1}
\frac{x^2+|x-1|-1}{x^2-x}
\)
Exercice 4
⭐ ⭐
avec solution
Calculer les limites :
\(
\displaystyle
\lim_{x\rightarrow+\infty}
\left(
\sqrt{x^2+4x-5}+x
\right)
\)
\(
\displaystyle
\lim_{x\rightarrow-\infty}
\left(
\sqrt{x^2-4x+7}-3x
\right)
\)
\(
\displaystyle
\lim_{x\rightarrow-\infty}
\left(
\sqrt{x^2+x-3}-3x
\right)
\)
\(
\displaystyle
\lim_{x\rightarrow-\infty}
\left(
\sqrt{x^2+5}+4x
\right)
\)
\(
\displaystyle
\lim_{x\rightarrow+\infty}
\left(
\sqrt{x^2-1}-x
\right)
\qquad
\lim_{x\rightarrow-\infty}
\left(
\sqrt{x^2+4x-3}+2x
\right)
\)
\(
\displaystyle
\lim_{x\rightarrow+\infty}
\left(
\frac{x}{3}+2+
\sqrt{\frac{x^2}{9}-2x+3}
\right)
\)
\(
\displaystyle
\lim_{x\rightarrow+\infty}
\left(
\sqrt{9x^2+x}
-
\sqrt{4x^2+3}
-
\sqrt{x^2+4}
\right)
\)
\(
\displaystyle
\lim_{x\rightarrow+\infty}
\frac{\sqrt{x^2+1}+x}{x+2}
\qquad
\lim_{x\rightarrow+\infty}
\frac{\sqrt{x}-1}{x+1}
\)
\(
\displaystyle
\lim_{x\rightarrow-\infty}
\frac{x-2}{\sqrt{9x^2+x}}
\qquad
\lim_{x\rightarrow+\infty}
\frac{\sqrt{x^2-4}}{1-\sqrt{x}}
\)
\(
\displaystyle
\lim_{x\rightarrow+\infty}
\frac{\sqrt{x}}
{\sqrt{x+\sqrt{x+\sqrt{x}}}}
\)
\(
\displaystyle
\lim_{x\rightarrow+\infty}
\frac{x}{\sqrt{x}-1}
\)
Exercice 5
⭐ ⭐
avec solution
Calculer les limites :
\(
\displaystyle
\lim_{x\rightarrow0}
\frac{\sin(2x)}{3x}
\qquad
\lim_{x\rightarrow0}
\frac{\tan(4x)}{5x}
\)
\(
\displaystyle
\lim_{x\rightarrow0}
\frac{\sin(2x)}{\tan(3x)}
\qquad
\lim_{x\rightarrow0}
\frac{x+\sin x}{x-\tan x}
\)
\(
\displaystyle
\lim_{x\rightarrow0}
\frac{1-\cos x}{x\tan(2x)}
\qquad
\lim_{x\rightarrow0}
\frac{\sin x-\cos x+1}{x}
\)
\(
\displaystyle
\lim_{x\rightarrow+\infty}
x^2
\left(
1-\cos\left(\frac{1}{x}\right)
\right)
\qquad
\lim_{x\rightarrow1}
\frac{x^2-1}{\sin(1-x)}
\)
\(
\displaystyle
\lim_{x\rightarrow\frac{\pi}{4}}
\frac{\sqrt{2}\cos x-1}
{x-\frac{\pi}{4}}
\)
\(
\displaystyle
\lim_{x\rightarrow\pi}
\frac{\cos x-1}{x-\pi}
\qquad
\lim_{x\rightarrow0}
\frac{\cos x-3}{x^2+1}
\)