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Question-56200

Question Number 56200 by naka3546 last updated on 11/Mar/19 Commented by Abdo msup. last updated on 12/Mar/19 $${changement}\:{x}={sin}\theta\:{give}\: \\ $$$${I}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{arcos}\left({cos}\theta\right){cos}\theta}{{cos}\theta}\:{d}\theta\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \theta\:{d}\theta \\…

Find-all-function-f-Q-R-such-that-f-a-f-b-a-b-2-a-b-Q-

Question Number 121714 by ZiYangLee last updated on 11/Nov/20 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{function}\:{f}:\mathrm{Q}\rightarrow\mathbb{R}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mid{f}\left({a}\right)−{f}\left({b}\right)\mid\leqslant\left({a}−{b}\right)^{\mathrm{2}\:} \forall\:{a},{b}\in\mathrm{Q} \\ $$ Answered by mindispower last updated on 11/Nov/20 $${f}\:{is}\:{continue} \\ $$$$\forall\epsilon>\mathrm{0}\:\exists\eta>\mathrm{0}\:\forall{x}\in{Q}\left[\mid{x}−{a}\mid<\eta\Rightarrow\mid{f}\left({x}\right)−{f}\left({a}\right)\mid<\epsilon\right.…

n-n-20-n-

Question Number 187215 by Humble last updated on 14/Feb/23 $$\frac{\sqrt{{n}!}}{{n}}=\sqrt{\mathrm{20}}\:;\:{n}=? \\ $$ Answered by ajfour last updated on 14/Feb/23 $$\frac{{n}!}{{n}^{\mathrm{2}} }=\mathrm{20} \\ $$$$\left({n}−\mathrm{1}\right)!=\mathrm{20}\left({n}−\mathrm{1}\right)+\mathrm{20} \\ $$$$\left({n}−\mathrm{2}\right)!=\mathrm{20}+\frac{\mathrm{20}}{{n}−\mathrm{1}}…

Question-187190

Question Number 187190 by 073 last updated on 14/Feb/23 Answered by aba last updated on 14/Feb/23 $$\mathrm{x}\Delta\mathrm{e}=\mathrm{x}\Rightarrow−\mathrm{3x}×\mathrm{e}−\mathrm{3x}−\mathrm{3e}−\mathrm{4}=\mathrm{x} \\ $$$$\Rightarrow−\mathrm{3e}\left(\mathrm{x}+\mathrm{1}\right)=\mathrm{4}\left(\mathrm{x}+\mathrm{1}\right)\Rightarrow\:\mathrm{e}=−\frac{\mathrm{4}}{\mathrm{3}} \\ $$ Commented by 073 last…

1-27-z-9-z-9-1-3-4-solve-for-z-

Question Number 56104 by problem solverd last updated on 10/Mar/19 $$\left(\frac{\mathrm{1}}{\mathrm{27}}\right)^{\mathrm{z}} +\mathrm{9}^{\mathrm{z}} .\mathrm{9}=\frac{\mathrm{1}}{\mathrm{3}^{−\mathrm{4}} } \\ $$$$\mathrm{solve}\:\mathrm{for}\:\mathrm{z} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 10/Mar/19…

Prove-that-If-a-set-consist-of-n-number-of-terms-then-its-Power-Set-would-contain-2-n-number-of-terms-Use-formulas-of-sequence-and-series-

Question Number 56075 by Kunal12588 last updated on 10/Mar/19 $${Prove}\:{that}\:{If}\:{a}\:{set}\:{consist}\:{of}\:{n}\:{number}\:{of} \\ $$$${terms}\:{then}\:{its}\:{Power}\:{Set}\:{would}\:{contain} \\ $$$$\mathrm{2}^{{n}} \:{number}\:{of}\:{terms}. \\ $$$$\left[{Use}\:{formulas}\:{of}\:{sequence}\:{and}\:{series}\right] \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on…