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Calculez \(\displaystyle\lim_{\stackrel{x \rightarrow 0}{x > 0}} \ln(\sin(x))\sin(x) \).
\(0\)
\(1\)
\(\infty\)
La limite n'existe pas.
Trouver l'ensemble \(S \) des \(x\) tels que \(e^x + e^{-x} = 2\).
\( S = \{0\} \)
\( S = \{1\} \)
\( S = \{\ln(2), -\ln(2)\} \)
\( S = \emptyset\)
Trouver l'ensemble \(S \) des \(x\) tels que \(e^{x} + 3e^{-x} > 4\).
\(S = ]-\infty, 0[ \)
\( S = ]\ln(3), +\infty[ \)
\(S = ]-\infty, 0[ \cup ]\ln(3), +\infty[ \)
\(S = ]-\infty, 1[ \cup ]3, +\infty[\)
Trouver l'ensemble \(S \) des \(x\) tels que \(\ln(-x) + \ln(x) = 0\).
\(S = \{-1\} \)
\( S = \{1\}\)
\( S = \emptyset \)
Trouver l'ensemble \(S \) des \(x\) tels que \(e^{2x} + 2 e^x + 1 = 0\).
\(S = \{0\}\)
\( S = \{\ln(2)\}\)
\(S = \{\ln(2), -\ln(2)\} \)
Trouver l'ensemble \(S \) des \(x\) tels que \(\log_2(x) = 2\log_2(3) - \log_2(x - 5) + 2\)
\( S = \{9\} \)
\(S = \{-4\} \)
\(S = \{-4, 9\} \)
\( S = \mathbb{R} \)
Calculez \(\displaystyle\lim_{x \rightarrow +\infty} \frac{\ln(x)}{x} \).
\(+\infty\)
Trouver l'ensemble \(S \) des \(x\) tels que \(\ln(x^2 - 3x - 3) > 0\).
\(S = ]0, +\infty[ \)
\( S = ]-\infty, 1[ \cup ]2,+ \infty[\)
\(S = ]-\infty, -1[ \cup ]4, +\infty[ \)
\(S = ]4, +\infty[ \)
Calculez \(\displaystyle\lim_{\stackrel{x \rightarrow 0}{x > 0}} x\ln(x) \).
\(1 \)
La limite n'a pas de sens.
Trouver l'ensemble \(S \) des \(x\) tels que \(\ln(5x) - \ln(x + 1) = \ln(2)\).
\(S = \{-1\}\)
\(S = \left\{\dfrac{1}{4}\right\} \)
\(S =\left \{\dfrac{1}{3}\right\} \)
\( S =\left \{\dfrac{2}{3}\right\} \)
