Exercice 1
Calculer : \(\lim_{x\to+\infty}(x^3 - 2x + 1)\), \(\lim_{x\to-\infty}(-2x^2 + x)\), \(\lim_{x\to+\infty}\frac{5x - 1}{2x + 3}\).
Correction
\(+\infty\) ; \(-\infty\) ; \(\frac52\).
Exercice 2
Calculer \(\lim_{x\to3}\frac{x^2 - 9}{x - 3}\).
Correction
\(\frac{(x - 3)(x + 3)}{x - 3} = x + 3\to6\).
Exercice 3
Calculer \(\lim_{x\to2^+}\frac{1}{x - 2}\) et \(\lim_{x\to2^-}\frac{1}{x - 2}\).
Correction
\(+\infty\) et \(-\infty\).
Exercice 4
Soit \(f(x) = \frac{3x + 2}{x - 1}\). Déterminer les asymptotes de sa courbe.
Correction
\(\lim_{x\to1^\pm}f = \pm\infty\) : asymptote \(x = 1\). \(\lim_{\pm\infty}f = 3\) : asymptote \(y = 3\).