Question Number 179961 by yaojunon2t last updated on 05/Nov/22 $${f}\left({x}\right)\in\left[\mathrm{0},\mathrm{1}\right],\mathrm{1}\leqslant{f}\left({x}\right)\leqslant\mathrm{3} \\ $$$${how}\:{to}\:{prove}\:\mathrm{1}\leqslant\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right){dx}\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{dx}}{{f}\left({x}\right)}\leqslant\frac{\mathrm{4}}{\mathrm{3}}? \\ $$ Answered by Frix last updated on 06/Nov/22…
Question Number 114433 by bemath last updated on 19/Sep/20 $${find}\:{sum}\:{of}\:{the}\:{series}\: \\ $$$$\mathrm{1}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} +\mathrm{5}^{\mathrm{2}} −\mathrm{7}^{\mathrm{2}} +\mathrm{9}^{\mathrm{2}} −\mathrm{11}^{\mathrm{2}} +…+\left(\mathrm{4}{n}−\mathrm{3}\right)^{\mathrm{2}} −\left(\mathrm{4}{n}−\mathrm{1}\right)^{\mathrm{2}} \\ $$ Answered by 1549442205PVT last…
Question Number 48884 by tanmay.chaudhury50@gmail.com last updated on 29/Nov/18 $${find}\:{last}\:{digit}\:{of} \\ $$$$\mathrm{1}!+\mathrm{2}!+\mathrm{3}!+\mathrm{4}!+…+\mathrm{23}! \\ $$$${and}\:\mathrm{1}!+\mathrm{2}!+\mathrm{3}!+…+\mathrm{134}! \\ $$ Answered by mr W last updated on 29/Nov/18 $${last}\:{digit}\:{of}\:{n}!\:{is}\:\mathrm{0}\:{for}\:{n}\geqslant\mathrm{5}.…
Question Number 48877 by absa last updated on 29/Nov/18 Commented by absa last updated on 29/Nov/18 $${find}\:{the}\:{inverse}\:{laplace}\:{transformation}? \\ $$ Answered by Abdulhafeez Abu qatada last…
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Question Number 179908 by Acem last updated on 04/Nov/22 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{Some}}\:\boldsymbol{{Important}}\:\boldsymbol{{notes}} \\ $$$$\:\mathrm{1}\boldsymbol{{st}}\:{Someone}\:{has}\:{solved}\:{a}\:{question}\:{as}\:{wrong}, \\ $$$$\:{and}\:{after}\:{he}\:{see}\:{other}\:{people}\:{have}\:{solved}\:{it} \\ $$$$\:{correctly}\:{he}\:{delete}\:{his}\:{poste}!\:{hmmm}\:{by}\:{the}\:{way}, \\ $$$$\:{i}\:{have}\:{some}\:{lapses},\:{i}'{ve}\:{never}\:{deleted}\:{any}. \\ $$$$\:{My}\:{mistakes}\:{keep}\:{you}\:{from}\:{making}\:{like}\:{them}. \\ $$$$\:{There}\:{is}\:{no}\:{embarrassment},\:{so}\:{please},\:{leave} \\ $$$$\:{things}\:{as}\:{they}\:{are}. \\…
Question Number 48833 by Tawa1 last updated on 29/Nov/18 Commented by Ali Yousafzai last updated on 29/Nov/18 Commented by Tawa1 last updated on 29/Nov/18 $$\mathrm{No}\:\mathrm{answer}\:\mathrm{there}\:\mathrm{sir}.\:\:\mathrm{I}\:\mathrm{dont}\:\mathrm{know}\:\mathrm{if}\:\mathrm{it}\:\mathrm{is}\:\mathrm{correct}\:\mathrm{but}\:\mathrm{i}\:\mathrm{will}\:\mathrm{use}\:\mathrm{your}\:\mathrm{work}.\:…
Question Number 48823 by tanmay.chaudhury50@gmail.com last updated on 29/Nov/18 Commented by Abdulhafeez Abu qatada last updated on 29/Nov/18 $${This}\:{intergrals}\:{i}\:{must}\:{try} \\ $$ Commented by Meritguide1234 last…
Question Number 48826 by ggny last updated on 29/Nov/18 $$\mathrm{2}\frac{\mathrm{5}}{\mathrm{7}}\:\:\:\:\:\:\:\:\:\:\:\mathrm{380} \\ $$$$\mathrm{8}\frac{\mathrm{3}}{\mathrm{7}}\:\:\:\:\:\:\:\:\:\:\:\:\:×\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{plz}\:{help}\:{me} \\ $$$$ \\ $$$$ \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 29/Nov/18…
Question Number 179886 by yaojunon2t last updated on 03/Nov/22 Commented by yaojunon2t last updated on 03/Nov/22 $$\because{e}^{{i}\theta} =\mathrm{cos}\:\theta+{i}\:\mathrm{sin}\:\theta,\theta=\frac{\pi}{\mathrm{2}}+\mathrm{2}{k}\pi \\ $$$$\therefore{e}^{{i}\left(\frac{\pi}{\mathrm{2}}+\mathrm{2}{k}\pi\right)} =\mathrm{cos}\:\frac{\pi}{\mathrm{2}}+{i}\:\mathrm{sin}\:\frac{\pi}{\mathrm{2}} \\ $$$$\therefore{e}^{{i}\left(\frac{\pi}{\mathrm{2}}+\mathrm{2}{k}\pi\right)} ={i} \\…