factoriser [tex] \frac{ \frac{2}{6+h} - \frac{1}{3} }{h} [/tex] SVP.... Pergunta de ideia delila98

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factoriser [tex] \frac{ \frac{2}{6+h} - \frac{1}{3} }{h} [/tex] SVP

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Cxrly $\frac{ \frac{2}{6+h} - \frac{1}{3} }{h}$
Tu met au même dénominateur :

= $\frac{ \frac{2(3)}{3(6+h)} - \frac{1(6+h)}{3(6+h)} }{h}$

= $\frac{ \frac{6}{18+3h} - \frac{6+h}{18+3h} }{h}$

= $\frac{ \frac{6-6-h}{18+3h} }{h}$

= $\frac{ \frac{-h}{18+3h} }{h}$

= $\frac{-h}{18+3h}$ x $\frac{1}{h}$

= $\frac{-1}{18+3h}$ (on a simplifier les h en haut et en bas)

Donc $\lim_{h \to \0}0$ $\frac{ \frac{2}{6+h} - \frac{1}{3} }{h}$

= $\lim_{h \to \0}0$ $\frac{-1}{18+3h}$

= $\frac{-1}{18}$

La fonction est dérivable sur R* et la dérivée est $\frac{-1}{18}$

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lila98 Merciiii beaucoup pour votre aide !!

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