Question

lim (r²-r)/(2r²+5r-7) r tende a 1

Answer 1

$r^2-r=r(r-1)\\ 2r^2+5r-7=0\ \to\ r=\dfrac{-5\pm\sqrt{25+56}}{4}=\dfrac{-5\pm9}{4}=\boxed{1}\ ou\ \boxed{-\dfrac{7}{2}}\ \to\\ \to\ 2r^2+5r-7=2(r-1)\bigg(r+\dfrac{7}{2}\bigg)=(r-1)(2r+7)\\\\ \lim_{r\to1}\dfrac{r^2-r}{2r^2+5r-7}=\lim_{r\to1}\dfrac{r(r-1)}{(r-1)(2r+7)}=\lim_{r\to1}\dfrac{r}{2r+7}=\\\\ =\dfrac{1}{2+7}=\boxed{\dfrac{1}{9}}$

Answer 2

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