Auto-Math
Simplifiez l'expression suivante : \( \ln{5}+\dfrac{1}{2}\ln{4} \).
\(10\)
\(\ln{10}\)
\(\ln{7}\)
\(\ln\left(\dfrac{5}{2}\right) \)
Trouvez l'ensemble \(S\) des \(x\) tels que \(\log_3(x) \geq -3 \).
\(S = \left\{\dfrac{1}{27}\right\}\)
\(S =\left ]0, \dfrac{1}{27}\right] \)
\(S = \left]\dfrac{1}{27}, +\infty\right[ \)
\(S =\left [\dfrac{1}{27}, +\infty\right[ \)
Calculer \(\displaystyle\lim_{x \to +\infty} \ln\left( \dfrac{1}{x} \right) \).
\(0\)
\(-\infty \)
\(+\infty\)
La limite n'existe pas.
Trouvez \(x\) si \((-2)^x = 4 \).
\(x = -2\)
\(x = 2\)
\(x = 4\)
Impossible
Trouvez l'ensemble \(S\) des \(x\) tels que \(\ln(x) > 0 \).
\(S = ]0, +\infty[ \)
\(S = ]1, +\infty[ \)
\(S = ]-\infty, 1[\)
\(S = ]-\infty, 0[ \)
Trouvez \(x\) si \(2^x = 4 \).
\(x = 0\)
\(x = 2 \)
Trouvez l'ensemble \(S\) des \( x\) tels que \(\ln\left(\dfrac{x + 3}{2}\right) = \dfrac{1}{2}(\ln(x) + \ln(3)) \).
\(S = \{3\}\)
\(S =\left \{\dfrac{3}{2}\right\}\)
\(S = \{-1 + \sqrt{3}, -1 - \sqrt{3}\}\)
\(S = \{-1 + \sqrt{3}\} \)
Calculer \(\displaystyle\lim_{x \to +\infty} e^x \).
\(-\infty\)
\(1 \)
Calculer \(\displaystyle\lim_{x \to 0} e^x \).
\(1\)
\(-1\)
Trouvez l'ensemble \(S\) des \(x\) tels que \(\log_4(x) < 5\).
\(S = \{1024\} \)
\(S = ]-\infty, 1024[ \)
\(S = ]0, 1024[ \)
\( S = ]1024, +\infty[ \)
