Bonjour,
En utilisant la règle de l'Hospital
[tex] \lim_{x \to \frac{5}{2}} \dfrac{\sqrt{2x+4} -\sqrt{2x-1} -1 }{ \sqrt{2x+11} -\sqrt{2x-1} -2} \\\\
=\lim_{x \to \frac{5}{2}} \dfrac{(\sqrt{2x+4} -\sqrt{2x-1} -1)' }{ (\sqrt{2x+11} -\sqrt{2x-1} -2)'} \\\\
[/tex]
[tex] = \lim_{x \to \frac{5}{2}}
\dfrac{
\dfrac{1} {\sqrt{2x+4} }-\dfrac{1} {\sqrt{2x-1} }
}
{\dfrac{1} {\sqrt{2x+11} }-\dfrac{1} {\sqrt{2x-1} } }\\\\
=\dfrac{\dfrac{1}{3}-\dfrac{1}{2}}{\dfrac{1}{4}-\dfrac{1}{2} }\\\\
=\dfrac{2}{3}\\\\
[/tex]
