Réponses

2014-02-15T23:57:06+01:00
Bonsoir,

Voici un exemple d'encadrement.

f(x)=\dfrac{\sqrt{2x+1}}{x^2+3}


1 < x < 2\Longrightarrow 2 < 2x < 4\Longrightarrow 3 < 2x+1 < 5\Longrightarrow \sqrt{3} < \sqrt{2x+1} < \sqrt{5}

1 < x < 2\Longrightarrow 1 < x^2 < 4\Longrightarrow 4 < x^2+3 < 7\Longrightarrow \dfrac{1}{7} < \dfrac{1}{x^2+3} < \dfrac{1}{4}

Par conséquent

\sqrt{3}\times\dfrac{1}{7} < \sqrt{2x+1}\times\dfrac{1}{x^2+3} < \sqrt{5}\times\dfrac{1}{4}\\\\\\\dfrac{\sqrt{3}}{7} < \dfrac{\sqrt{2x+1}}{x^2+3} < \dfrac{\sqrt{5}}{4}\\\\\\\dfrac{\sqrt{3}}{7} < f(x) < \dfrac{\sqrt{5}}{4}