Question Number 67136 by ,jamiebots last updated on 23/Aug/19 $${factorize}\:\mathrm{2}{x}^{\mathrm{3}} −\mathrm{1} \\ $$ Answered by Cmr 237 last updated on 23/Aug/19 $$\mathrm{2x}^{\mathrm{3}} −\mathrm{1}=\mathrm{2}\left(\mathrm{x}^{\mathrm{3}} −\frac{\mathrm{1}}{\mathrm{2}}\right)=\mathrm{p}\left(\mathrm{x}\right) \\…
Question Number 132674 by aurpeyz last updated on 15/Feb/21 $${integral}\:{of}\:{e}^{−\mathrm{2}{ax}^{\mathrm{2}} } \\ $$ Answered by Olaf last updated on 15/Feb/21 $$\mathrm{Let}\:\Omega_{{a}} \left({x}\right)\:=\:\int_{\mathrm{0}} ^{{x}} {e}^{−\mathrm{2}{at}^{\mathrm{2}} }…
Question Number 1597 by Rasheed Ahmad last updated on 25/Aug/15 $$\int\frac{{f}\left({x}\right)}{{f}\:'\left({x}\right)}{dx}={ln}\:{sec}\:{x}+{c} \\ $$$${f}\left({x}\right)=? \\ $$ Answered by 123456 last updated on 25/Aug/15 $$\int\frac{{y}}{{dy}/{dx}}{dx}=\mathrm{ln}\:\mathrm{sec}\:{x}+{c} \\ $$$$\frac{{d}}{{dx}}\left[\int\frac{{y}}{{dy}/{dx}}{dx}\right]=\frac{{d}}{{dx}}\left[\mathrm{ln}\:\mathrm{sec}\:{x}+{c}\right]…
Question Number 1594 by 123456 last updated on 24/Aug/15 $${f}\left({x}\right)=\underset{\mathrm{0}} {\overset{{x}} {\int}}{t}^{{x}} {dt},{x}>−\mathrm{1} \\ $$$$\underset{{x}\rightarrow−\mathrm{1}^{+} } {\mathrm{lim}}{f}\left({x}\right)=? \\ $$$${f}\left({x}+\mathrm{1}\right)−{f}\left({x}\right)=? \\ $$ Commented by 112358 last…
Question Number 1592 by Rasheed Soomro last updated on 23/Aug/15 $$\mathrm{I}\:\mathrm{have}\:\mathrm{a}\:\mathrm{loop}\:\mathrm{of}\:\mathrm{string}\:\mathrm{of}\:\mathrm{length}\left(\mathrm{perimeter}\right)\:\:\mathrm{p}\:\mathrm{units}.\: \\ $$$$\mathrm{I}\:\mathrm{want}\:\mathrm{to}\:\mathrm{make}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{of}\:\mathrm{largest}\:\mathrm{area}\:\mathrm{from}\:\mathrm{the} \\ $$$$\mathrm{loop}.\:\mathrm{What}\:\mathrm{will}\:\mathrm{be}\:\mathrm{the}\:\mathrm{dimensions}\:\mathrm{of}\:\mathrm{that}\:\mathrm{triangle}? \\ $$ Commented by 123456 last updated on 23/Aug/15 $${x}+{y}+{z}={p}…
Question Number 67122 by sandeepkeshari0797@gmail.com last updated on 23/Aug/19 Answered by Cmr 237 last updated on 23/Aug/19 $$\mathrm{y}_{\mathrm{n}+\mathrm{2}} −\mathrm{2y}_{\mathrm{n}+\mathrm{1}} +\mathrm{y}_{\mathrm{n}} −\mathrm{n}^{\mathrm{2}} \mathrm{2}^{\mathrm{n}} =\mathrm{0} \\ $$$$\mathrm{l}'\mathrm{equation}\:\mathrm{caracteristique}\:\mathrm{est}:…
Question Number 1585 by Rasheed Soomro last updated on 22/Aug/15 $$\mathrm{Let}\:\omega\:\mathrm{is}\:\mathrm{cube}\:\mathrm{root}\:\mathrm{of}\:\mathrm{unity}\:\mathrm{and}\:\mathrm{x},\mathrm{y},\mathrm{z}\:\in\:\mathbb{Z} \\ $$$$\mathrm{If}\:\omega^{\mathrm{x}} +\omega^{\mathrm{y}} +\omega^{\mathrm{z}} =\mathrm{0}\:\mathrm{prove}\:\mathrm{that}\:\mathrm{3}\:\mid\:\left(\mathrm{x}+\mathrm{y}+\mathrm{z}\right) \\ $$$$\mathrm{Show}\:{by}\:{an}\:{example}\:\mathrm{that}\:\mathrm{the}\:\mathrm{converse}\:\mathrm{is}\:{not}\:\:\mathrm{true}. \\ $$ Commented by 112358 last updated…
Question Number 132652 by Salman_Abir last updated on 15/Feb/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 1582 by 112358 last updated on 21/Aug/15 $${Let}\:\phi\:{and}\:\varepsilon\:{denote}\:{functions}\:{of}\:{x} \\ $$$${where}\:\phi\:{is}\:{odd}\:{and}\:\varepsilon\:{is}\:{even}\:\forall{x}\in\mathbb{R}. \\ $$$${Is}\:{it}\:{generally}\:{true}\:{that}\:{integrating} \\ $$$${an}\:{odd}\:{function}\:{gives}\:{an}\:{even} \\ $$$${function}\:{and}\:{vice}\:{versa}?\: \\ $$$$\int\phi_{\mathrm{1}} \left({x}\right)\:{dx}=\varepsilon_{\mathrm{1}} \left({x}\right)+{C}\:? \\ $$$${and}\:\int\phi_{\mathrm{2}} \left({x}\right){dx}=\varepsilon_{\mathrm{2}}…
Question Number 132655 by mohammad17 last updated on 15/Feb/21 $${write}\:\frac{\left(\mathrm{1}−{i}\right)^{\mathrm{23}} }{\left(\sqrt{\mathrm{3}}−{i}\right)^{\mathrm{13}} }\:{by}\:{re}^{{i}\theta} \:{such}\:{that}\:{r}>\mathrm{0},−\pi\leqslant\theta<\pi \\ $$ Answered by physicstutes last updated on 15/Feb/21 $$\mathrm{1}\:−{i}\:=\:\sqrt{\mathrm{2}}\:{e}^{−\frac{\pi}{\mathrm{4}}{i}} \\ $$$$\Rightarrow\:\left(\mathrm{1}−{i}\right)^{\mathrm{23}}…