Question Number 133692 by Dwaipayan Shikari last updated on 23/Feb/21 $$\frac{{sin}\mathrm{1}}{{e}}−\frac{{sin}\left(\mathrm{2}\right)}{\mathrm{2}{e}^{\mathrm{2}} }+\frac{{sin}\left(\mathrm{3}\right)}{\mathrm{3}{e}^{\mathrm{3}} }−\frac{{sin}\left(\mathrm{4}\right)}{\mathrm{4}{e}^{\mathrm{4}} }+…={tan}^{−\mathrm{1}} \left(\frac{{sin}\left(\mathrm{1}\right)}{{cos}\left(\mathrm{1}\right)+{e}}\right) \\ $$ Commented by Dwaipayan Shikari last updated on 23/Feb/21…
Question Number 2524 by 123456 last updated on 21/Nov/15 $${f}:\mathbb{R}^{\mathrm{2}} \rightarrow\mathbb{R} \\ $$$${f}\left({x},{y}\right)={x}^{\mathrm{2}} −{y}^{\mathrm{2}} \:\:\:\:\:\:\:\:\:\:{y}\geqslant\mathrm{0} \\ $$$${f}\left({x},{y}\right)={x}^{\mathrm{2}} +{y}^{\mathrm{2}} \:\:\:\:\:\:\:\:\:\:{y}\leqslant\mathrm{0} \\ $$$$\mathrm{find} \\ $$$$\left({x},{y}\right)\:\mathrm{for}\:\mathrm{min}\:{f}\left({x},{y}\right) \\ $$$$\left({x},{y}\right)\:\mathrm{for}\:{f}\left({x},{y}\right)=\mathrm{1}…
Question Number 133590 by physicstutes last updated on 23/Feb/21 $$\mathrm{A}\:\mathrm{particle}\:\mathrm{performs}\:\mathrm{simple}\:\mathrm{harmonic}\:\mathrm{motion}\:\mathrm{between}\:\mathrm{two}\:\mathrm{points} \\ $$$$\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{which}\:\mathrm{are}\:\mathrm{10}\:\mathrm{m}\:\mathrm{apart}\:\mathrm{on}\:\mathrm{a}\:\mathrm{horizontal}\:\mathrm{straight}\:\mathrm{line}. \\ $$$$\mathrm{When}\:\mathrm{the}\:\mathrm{particle}\:\mathrm{is}\:\mathrm{3}\:\mathrm{m}\:\mathrm{away}\:\mathrm{from}\:\mathrm{the}\:\mathrm{centre},\:\mathrm{O},\:\mathrm{of}\:\mathrm{the}\:\mathrm{line}\:\mathrm{AB}, \\ $$$$\mathrm{its}\:\mathrm{speed}\:\mathrm{is}\:\mathrm{8}\:\mathrm{ms}^{−\mathrm{1}} .\:\mathrm{Find}\:\mathrm{the}\:\mathrm{least}\:\mathrm{time}\:\mathrm{required}\:\mathrm{for}\:\mathrm{the} \\ $$$$\mathrm{particle}\:\mathrm{to}\:\mathrm{move}\:\mathrm{from}\:\mathrm{B}\:\mathrm{to}\:\mathrm{the}\:\mathrm{midpoint}\:\mathrm{of}\:\mathrm{OA}. \\ $$ Answered by mr W…
Question Number 2514 by 123456 last updated on 21/Nov/15 $$\mathrm{is}\:\mathrm{there}\:\mathrm{a}\:\mathrm{function} \\ $$$${f}:\mathbb{R}^{\mathrm{2}} \rightarrow\mathbb{R} \\ $$$$\mathrm{such}\:\mathrm{that} \\ $$$${f}\left[{x},{f}\left({x},{y}\right)\right]={f}\left[{f}\left({x},{y}\right),{y}\right]={f}\left({x},{y}\right) \\ $$$$? \\ $$ Answered by prakash jain…
Question Number 2504 by 123456 last updated on 21/Nov/15 $${f}\left({x},{y}\right)={f}\left({x},{y}−{x}\right) \\ $$$${f}\left({x},{y}\right)={f}\left({y},{x}\right) \\ $$$${f}\left(\mathrm{0},{y}\right)={y}^{\mathrm{2}} \\ $$$$\mathrm{does} \\ $$$${g}\left({x}\right):={f}\left({x},{x}\right) \\ $$$${g}\left(−{x}\right)\overset{?} {=}{g}\left({x}\right) \\ $$$${f}\left(\mathrm{10},\mathrm{5}\right)=? \\ $$…
Question Number 133482 by AbderrahimMaths last updated on 22/Feb/21 $$\:\:\:\:{we}\:{consider}\:{that}\:{application}\:{n}\geqslant\mathrm{1} \\ $$$$\:\:{det}\::\:{M}_{{n}} \left(\mathbb{R}\right)\rightarrow\mathbb{R} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{A} {det}\left({A}\right) \\ $$$$\mathrm{1}−{verify}\:{that}\:\forall{H}\in{M}_{{n}} \left(\mathbb{R}\right)\:{and}\:{t}\in\mathbb{R} \\ $$$$\:{if}\:{A}={I}_{{n}} \Rightarrow{det}\left({A}+{tH}\right)=\mathrm{1}+{t}.{Tr}\left({H}\right)+\circ\left({t}\right) \\ $$$$\mathrm{2}−{suppose}\:{that}:\:{A}\in{GL}_{{n}} \left(\mathbb{R}\right)…
Question Number 67927 by Rasheed.Sindhi last updated on 02/Sep/19 $$\mathrm{Tinku}\:\mathrm{Tara},\mathrm{the}\:\mathrm{developer}. \\ $$$$\mathrm{Sir}, \\ $$$$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{receive}\:\mathrm{notifications}\:\mathrm{from} \\ $$$$\mathrm{the}\:\mathrm{forum}.\mathrm{Pl}\:\mathrm{fix}\:\mathrm{the}\:\mathrm{problem}. \\ $$ Commented by TawaTawa last updated on 02/Sep/19…
Question Number 2393 by 123456 last updated on 19/Nov/15 $${f}:\left[\mathrm{0},\mathrm{1}\right]\rightarrow\mathbb{R} \\ $$$${x}={a}_{\mathrm{0}} ,{a}_{\mathrm{1}} {a}_{\mathrm{2}} {a}_{\mathrm{3}} … \\ $$$${f}\left({x}\right)=\underset{{i}=\mathrm{0}} {\overset{+\infty} {\sum}}{a}_{{i}} \\ $$$$\mathrm{is}\:{f}\left({x}\right)\:\mathrm{continuous}\:\mathrm{in}\:\mathrm{all}\:{x}\in\left[\mathrm{0},\mathrm{1}\right] \\ $$$${f}\left(\mathrm{0},\mathrm{9999}…\right)=?? \\…
Question Number 2384 by 123456 last updated on 18/Nov/15 $$\lfloor\mathrm{0},\mathrm{9999}….\rfloor=\mathrm{1}\:\mathrm{or}\:\mathrm{0}? \\ $$ Answered by Filup last updated on 19/Nov/15 $$\mathrm{0}.\overset{−} {\mathrm{9}}=\mathrm{1}\:\left(\mathrm{through}\:\mathrm{algerbraic}\:\mathrm{menipulation}\right) \\ $$$$\therefore\lfloor\mathrm{0}.\overset{−} {\mathrm{9}}\rfloor=\lfloor\mathrm{1}\rfloor=\mathrm{1} \\…
Question Number 67903 by rajesh4661kumar@gmail.com last updated on 02/Sep/19 Answered by $@ty@m123 last updated on 02/Sep/19 $${Let}\:\sqrt{{x}}={y} \\ $$$$\mathrm{3}{y}^{\mathrm{2}} +\frac{\mathrm{2}}{{y}}=\mathrm{1} \\ $$$$\mathrm{3}{y}^{\mathrm{3}} +\mathrm{2}={y} \\ $$$$\mathrm{3}{y}^{\mathrm{3}}…