Menu Close

Category: Others

f-x-y-f-x-y-x-f-x-y-f-y-x-f-0-y-y-2-does-g-x-f-x-x-g-x-g-x-f-10-5-

Question Number 2504 by 123456 last updated on 21/Nov/15 $${f}\left({x},{y}\right)={f}\left({x},{y}−{x}\right) \\ $$$${f}\left({x},{y}\right)={f}\left({y},{x}\right) \\ $$$${f}\left(\mathrm{0},{y}\right)={y}^{\mathrm{2}} \\ $$$$\mathrm{does} \\ $$$${g}\left({x}\right):={f}\left({x},{x}\right) \\ $$$${g}\left(−{x}\right)\overset{?} {=}{g}\left({x}\right) \\ $$$${f}\left(\mathrm{10},\mathrm{5}\right)=? \\ $$…

we-consider-that-application-n-1-det-M-n-R-R-A-det-A-1-verify-that-H-M-n-R-and-t-R-if-A-I-n-det-A-tH-1-t-Tr-H-t-2-suppose-that-A-GL-n-R-prouve-that-the-d

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)…

Tinku-Tara-the-developer-Sir-I-don-t-receive-notifications-from-the-forum-Pl-fix-the-problem-

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…

f-0-1-R-x-a-0-a-1-a-2-a-3-f-x-i-0-a-i-is-f-x-continuous-in-all-x-0-1-f-0-9999-f-1-1-

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)=?? \\…

0-9999-1-or-0-

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-67903

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}}…

sin-pi-1-3-sin-4pi-2-3-sin-9pi-3-3-sin-16pi-4-3-pi-pi-12-1-3-pi-2pi-

Question Number 133432 by Dwaipayan Shikari last updated on 22/Feb/21 $$\frac{{sin}\sqrt{\pi}}{\mathrm{1}^{\mathrm{3}} }+\frac{{sin}\sqrt{\mathrm{4}\pi}}{\mathrm{2}^{\mathrm{3}} }+\frac{{sin}\sqrt{\mathrm{9}\pi}}{\mathrm{3}^{\mathrm{3}} }+\frac{{sin}\sqrt{\mathrm{16}\pi}}{\mathrm{4}^{\mathrm{3}} }+….=\frac{\pi\sqrt{\pi}}{\mathrm{12}}\left(\mathrm{1}−\mathrm{3}\sqrt{\pi}+\mathrm{2}\pi\right) \\ $$ Answered by mindispower last updated on 24/Feb/21 $$\underset{{n}\geqslant\mathrm{0}}…

f-C-C-a-b-R-2-a-lt-b-f-z-a-f-b-z-sin-zpi-b-a-f-z-z-2-z-a-b-2-f-z-0-z-

Question Number 2362 by 123456 last updated on 18/Nov/15 $${f}:\mathbb{C}\rightarrow\mathbb{C},\left({a},{b}\right)\in\mathbb{R}^{\mathrm{2}} ,{a}<{b} \\ $$$${f}\left({z}−{a}\right)={f}\left({b}−{z}\right)\mathrm{sin}\:\frac{{z}\pi}{{b}−{a}} \\ $$$${f}\left({z}\right)={z}^{\mathrm{2}} ,\Re\left({z}\right)\geqslant\frac{{a}+{b}}{\mathrm{2}} \\ $$$${f}\left({z}\right)=\mathrm{0},{z}=? \\ $$ Commented by Rasheed Soomro last…