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Question-132194

Question Number 132194 by aurpeyz last updated on 12/Feb/21 Commented by mr W last updated on 12/Feb/21 $$\frac{{d}\theta}{{dr}}=\mathrm{3}{r}^{\mathrm{2}} −\mathrm{1} \\ $$$$\Delta\theta\approx\left(\mathrm{3}{r}^{\mathrm{2}} −\mathrm{1}\right)\Delta{r}=\left(\mathrm{3}×\mathrm{1}^{\mathrm{2}} −\mathrm{1}\right)×\mathrm{0}.\mathrm{05}=\mathrm{0}.\mathrm{1} \\ $$…

given-f-R-R-f-x-a-n-x-n-a-0-with-a-n-0-a-i-R-i-0-1-n-n-N-supose-that-x-1-x-n-are-roots-the-n-roots-of-f-x-then-proof-or-give-a-counter-example-that-the-root-of-f-n-1-x-

Question Number 1120 by 123456 last updated on 17/Jun/15 $$\mathrm{given}\:{f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${f}\left({x}\right)={a}_{{n}} {x}^{{n}} +\centerdot\centerdot\centerdot+{a}_{\mathrm{0}} \: \\ $$$$\mathrm{with}\:{a}_{{n}} \neq\mathrm{0},\:{a}_{{i}} \in\mathbb{R},{i}\in\left\{\mathrm{0},\mathrm{1},…,{n}\right\},{n}\in\mathbb{N}^{\ast} \\ $$$$\mathrm{supose}\:\mathrm{that}\:{x}_{\mathrm{1}} ,…,{x}_{{n}} \\ $$$$\mathrm{are}\:\mathrm{roots}\:\mathrm{the}\:{n}\:\mathrm{roots}\:\mathrm{of}\:{f}\left({x}\right) \\…

solve-2sec-2-x-2-2-3-secx-3-2-0-0-x-pi-4-

Question Number 132180 by bounhome last updated on 12/Feb/21 $${solve}\:: \\ $$$$\mathrm{2}{sec}^{\mathrm{2}} {x}+\left(\mathrm{2}\sqrt{\mathrm{2}}−\mathrm{3}\right){secx}−\mathrm{3}\sqrt{\mathrm{2}}=\mathrm{0}\:;\:\mathrm{0}\leqslant{x}\leqslant\frac{\pi}{\mathrm{4}} \\ $$ Answered by benjo_mathlover last updated on 12/Feb/21 $$\:\mathrm{3}\sqrt{\mathrm{2}}\:\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}−\left(\mathrm{2}\sqrt{\mathrm{2}}−\mathrm{3}\right)\mathrm{cos}\:\mathrm{x}−\mathrm{2}=\mathrm{0} \\…