Question Number 1139 by 314159 last updated on 30/Jun/15 $${Given}\:{that}\:{f}\:{is}\:{a}\:{polynomial}\:{function}\:{of} \\ $$$${degree}\:\mathrm{8}\:{such}\:{that}\:{f}\left(\mathrm{1}\right)=\frac{\mathrm{1}}{\mathrm{2}},{f}\left(\mathrm{2}\right)=\frac{\mathrm{1}}{\mathrm{6}},{f}\left(\mathrm{3}\right)=\frac{\mathrm{1}}{\mathrm{12}} \\ $$$${f}\left(\mathrm{4}\right)=\frac{\mathrm{1}}{\mathrm{20}},{f}\left(\mathrm{5}\right)=\frac{\mathrm{1}}{\mathrm{30}},{f}\left(\mathrm{6}\right)=\frac{\mathrm{1}}{\mathrm{42}},{f}\left(\mathrm{7}\right)=\frac{\mathrm{1}}{\mathrm{56}},{f}\left(\mathrm{8}\right)=\frac{\mathrm{1}}{\mathrm{72}} \\ $$$${f}\left(\mathrm{9}\right)=\frac{\mathrm{1}}{\mathrm{90}\:}\:\:.{Find}\:{f}\left(\mathrm{10}\right)\:{and}\:{f}\left(\mathrm{11}\right). \\ $$ Commented by 123456 last updated on 30/Jun/15…
Question Number 1134 by 314159 last updated on 28/Jun/15 $${Find}\:{the}\:{infinite}\:{product}\:{of}\: \\ $$$$\frac{\mathrm{3}}{\mathrm{2}}×\frac{\mathrm{5}}{\mathrm{4}}×\frac{\mathrm{17}}{\mathrm{16}}×\frac{\mathrm{257}}{\mathrm{256}}×\frac{\mathrm{65537}}{\mathrm{65536}}×… \\ $$ Answered by prakash jain last updated on 29/Jun/15 $$\frac{\mathrm{2}^{\mathrm{2}} −\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{2}^{\mathrm{2}} +\mathrm{1}}{\mathrm{2}^{\mathrm{2}}…
Question Number 132173 by I want to learn more last updated on 11/Feb/21 $$\mathrm{If}\:\:\:\:\mathrm{v}\:\:\:=\:\:\:\frac{\sqrt{\mathrm{p}\:\:\:+\:\:\:\frac{\mathrm{1}}{\mathrm{n}}}}{\mathrm{x}},\:\:\:\:\:\:\:\:\:\mathrm{where}\:\:\:\:\mathrm{p}\:\:=\:\:\:\mathrm{pressure}. \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{dimension}\:\mathrm{of}\:\:\:\:\:\mathrm{n}\:\:\:\mathrm{and}\:\:\:\mathrm{x} \\ $$ Commented by mr W last updated on…
Question Number 132162 by Dwaipayan Shikari last updated on 11/Feb/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{sin}\left({n}\right)}{{n}^{\mathrm{2}} } \\ $$ Answered by mnjuly1970 last updated on 11/Feb/21 $$\frac{\mathrm{1}}{\mathrm{2}{i}}\left[{li}_{\mathrm{2}} \left({e}^{{i}}…
Question Number 1068 by 123456 last updated on 01/Jun/15 $${f}:\mathbb{R}\rightarrow\mathbb{R}_{+} ,{g}:\mathbb{R}\rightarrow\mathbb{R}_{+} \\ $$$$\mathrm{2}{f}\left({x}\right)={f}\left({x}−\mathrm{1}\right)+{g}\left({x}+\mathrm{1}\right) \\ $$$$\left[{g}\left({x}\right)\right]^{\mathrm{2}} ={f}\left({x}−\mathrm{1}\right){g}\left({x}+\mathrm{1}\right) \\ $$$${f}\left(−\mathrm{1}\right)=\mathrm{1},{g}\left(\mathrm{1}\right)=\mathrm{2},{f}\left(\mathrm{0}\right){g}\left(\mathrm{0}\right)=? \\ $$ Answered by prakash jain last…
Question Number 1066 by 123456 last updated on 27/May/15 $$\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\frac{{x}}{\mathrm{tan}\:{x}}{dx} \\ $$ Answered by malwaan last updated on 01/Jun/15 $$\frac{\pi}{\mathrm{2}}{log}\left(\mathrm{2}\right) \\ $$ Terms…
Question Number 1057 by 123456 last updated on 25/May/15 $${f}:\mathbb{R}_{+} \rightarrow\mathbb{R} \\ $$$${x}={i}+{j} \\ $$$${x}\in\mathbb{R}_{+} \\ $$$${i}\in\mathbb{N} \\ $$$${j}\in\left[\mathrm{0},\mathrm{1}\right) \\ $$$${f}\left({x}\right)=\begin{cases}{{f}\left({i}−\mathrm{1}\right)+\left({i}+\mathrm{1}\right)\left({j}+\mathrm{1}\right)}&{{x}\geqslant\mathrm{1}}\\{{j}}&{\mathrm{0}\leqslant{x}<\mathrm{1}}\\{{x}}&{{x}<\mathrm{0}}\end{cases} \\ $$$${f}\left(\mathrm{9}.\mathrm{5}\right)=? \\ $$…
Question Number 132124 by Chhing last updated on 11/Feb/21 $$ \\ $$$$\:\:\:\mathrm{Calculate} \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \sqrt{\frac{\mathrm{tan}\left(\mathrm{x}\right)+\mathrm{tan}^{\mathrm{2}} \left(\mathrm{x}\right)}{\mathrm{tan}\left(\mathrm{x}\right)−\mathrm{tan}^{\mathrm{2}} \left(\mathrm{x}\right)}}\:\mathrm{cos}\left(\mathrm{x}\right)\mathrm{dx} \\ $$$$\:\: \\ $$ Commented by liberty…
Question Number 1039 by tera last updated on 22/May/15 $${jumlah}\:{akar}−{akar}\:{persamaan}\:\left[{x}\right]^{\mathrm{2}} −\mathrm{2}\left[{x}\right]−\mathrm{3}=\mathrm{0}\:{sama}\:{dengan} \\ $$$${a}.−\mathrm{10}\:\:\:\:\:\:\:\:\:\:{b}.−\mathrm{3}\:\:\:\:\:\:{e}.\mathrm{4} \\ $$$${c}.−\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:{d}.\mathrm{0} \\ $$ Commented by prakash jain last updated on 22/May/15…
Question Number 1030 by 123456 last updated on 20/May/15 $$\frac{{dy}}{{dt}}−\frac{{dx}}{{dt}}=\frac{{t}\frac{{dy}}{{dt}}+{y}}{{t}\frac{{dx}}{{dt}}+{x}} \\ $$ Answered by prakash jain last updated on 21/May/15 $${y}={k}_{\mathrm{1}} {t},{x}={k}_{\mathrm{2}} {t} \\ $$$$\frac{{dy}}{{dt}}={k}_{\mathrm{1}}…