Question Number 106690 by M±th+et+s last updated on 06/Aug/20 $${this}\:{question}\:{was}\:{repeatd}\:{six}\:{times} \\ $$$${in}\:{a}\:{various}\:{exams}\:{between}\:\mathrm{1971}\:{to}\:\mathrm{2001}. \\ $$$${if}\:{C}_{\mathrm{0}} ,{C}_{\mathrm{1}} ,{C}_{\mathrm{2}} …….,{C}_{{n}} \:{are}\:{the}\:{coefficients} \\ $$$${in}\:{the}\:{expansion}\:{of}\:\left(\mathrm{1}+{x}\right)^{{n}} \:{then} \\ $$$${c}_{\mathrm{0}} +\mathrm{2}{C}_{\mathrm{1}} +\mathrm{3}{C}_{\mathrm{2}}…
Question Number 106677 by mohammad17 last updated on 06/Aug/20 Answered by Dwaipayan Shikari last updated on 06/Aug/20 $$\left.\mathrm{5}\right)\int_{\mathrm{1}} ^{\mathrm{4}} \left(\mathrm{1}−{u}\right)\sqrt{{u}}{du} \\ $$$$\int_{\mathrm{1}} ^{\mathrm{4}} \sqrt{{u}}−{u}^{\frac{\mathrm{3}}{\mathrm{2}}} {du}…
Question Number 106662 by mathdave last updated on 06/Aug/20 Answered by Ar Brandon last updated on 06/Aug/20 $$\mathrm{Let}\:\mathrm{A}_{\mathrm{n}} =\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{ln}\left(\mathrm{x}!\right)^{\frac{\mathrm{1}}{\mathrm{x}}} \:,\:\mathrm{x}\in\mathbb{N} \\ $$$$\mathrm{lnx}!=\mathrm{ln}\left(\left(\mathrm{x}\right)\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}−\mathrm{2}\right)…\left(\mathrm{x}−\left(\mathrm{x}−\mathrm{1}\right)\right)\right) \\ $$$$\:\:\:\:\:\:\:\:\:=\mathrm{ln}\underset{\mathrm{k}=\mathrm{0}}…
Question Number 106654 by mohammad17 last updated on 06/Aug/20 Answered by bemath last updated on 06/Aug/20 $$\mathrm{total}\:\mathrm{area}\:=\:\mathrm{2}\underset{\mathrm{0}} {\overset{\mathrm{2}} {\int}}\left(\mathrm{4}−\mathrm{x}^{\mathrm{2}} \right)\mathrm{dx}\: \\ $$$$=\:\mathrm{2}\mid\left(\mathrm{4x}−\frac{\mathrm{1}}{\mathrm{3}}\mathrm{x}^{\mathrm{3}} \right)\mid_{\mathrm{0}} ^{\mathrm{2}} =\mathrm{2}\left(\mathrm{8}−\frac{\mathrm{8}}{\mathrm{3}}\right)=\frac{\mathrm{32}}{\mathrm{3}}…
Question Number 106648 by Tinku Tara last updated on 06/Aug/20 $$\mathrm{App}\:\mathrm{Updates}: \\ $$$$\mathrm{Please}\:\mathrm{update}\:\mathrm{to}\:\mathrm{latest}\:\mathrm{version}\:\mathrm{of} \\ $$$$\mathrm{app}\:\mathrm{2}.\mathrm{132}.\:\mathrm{It}\:\mathrm{fixes}\:\mathrm{some}\:\mathrm{bugs}\:\mathrm{and} \\ $$$$\mathrm{characters}\:\mathrm{drawing}\:\mathrm{is}\:\mathrm{also}\:\mathrm{improved} \\ $$$$\mathrm{so}\:\mathrm{characters}\:\mathrm{will}\:\mathrm{now}\:\mathrm{appear}\:\mathrm{smooth}. \\ $$$$\mathrm{Download}\:\mathrm{from}\:\mathrm{playstore}. \\ $$ Commented by…
Question Number 106644 by ZiYangLee last updated on 06/Aug/20 $$\mathrm{Let}\:\mathrm{P}\left(\mathrm{x}\right)\:\mathrm{be}\:\mathrm{a}\:\mathrm{polynomial}\:\mathrm{of}\:\mathrm{degree}\:\mathrm{n} \\ $$$$\mathrm{with}\:\mathrm{real}\:\mathrm{coefficients}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{P}^{\left(\mathrm{k}\right)} \left(\mathrm{0}\right)}{\left(\mathrm{k}+\mathrm{1}\right)!}=\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\frac{\left(−\mathrm{1}\right)^{\mathrm{k}} \mathrm{P}^{\left(\mathrm{k}\right)} \left(\mathrm{1}\right)}{\left(\mathrm{k}+\mathrm{1}\right)!} \\ $$$$ \\ $$…
Question Number 41108 by mondodotto@gmail.com last updated on 02/Aug/18 $$\boldsymbol{\mathrm{evaluate}}\:\int\boldsymbol{{x}}^{\boldsymbol{{i}}} \boldsymbol{{dx}} \\ $$$$\boldsymbol{\mathrm{where}}\:\boldsymbol{{i}}=\sqrt{−\mathrm{1}} \\ $$ Answered by MJS last updated on 02/Aug/18 $$\int{x}^{{z}} {dx}=\frac{\mathrm{1}}{{z}+\mathrm{1}}{x}^{{z}+\mathrm{1}} \\…
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Question Number 172152 by Giantyusuf last updated on 23/Jun/22 Answered by Rasheed.Sindhi last updated on 23/Jun/22 $${h}:\:{first}\:{digit}\left({hundred}\right) \\ $$$${t}:\:{second}\:{digit}\left({ten}\right) \\ $$$${u}:\:{third}\:{digit}\left({unit}\right) \\ $$$${t}=\mathrm{4}{u} \\ $$$${h}={t}−\mathrm{3}=\mathrm{4}{u}−\mathrm{3}…
Question Number 172151 by Giantyusuf last updated on 23/Jun/22 $$\mathrm{3}^{{x}} =\mathrm{10}−{log}_{\mathrm{2}} {x} \\ $$$${find}\:{x} \\ $$ Answered by aleks041103 last updated on 23/Jun/22 $$\mathrm{3}^{{x}} \:{is}\:{monotounously}\:{increasing}.…