Question Number 140981 by EnterUsername last updated on 14/May/21 $$\mathrm{Let}\:\alpha\neq\mathrm{1}\:\mathrm{and}\:\alpha^{\mathrm{13}} =\mathrm{1}.\:\mathrm{If}\:{a}=\alpha+\alpha^{\mathrm{3}} +\alpha^{\mathrm{4}} +\alpha^{−\mathrm{4}} +\alpha^{−\mathrm{3}} + \\ $$$$\alpha^{−\mathrm{1}} \:\mathrm{and}\:{b}=\alpha^{\mathrm{2}} +\alpha^{\mathrm{5}} +\alpha^{\mathrm{6}} +\alpha^{−\mathrm{6}} +\alpha^{−\mathrm{5}} +\alpha^{−\mathrm{2}} \:\mathrm{then}\:\mathrm{the} \\…
Question Number 75446 by Crabby89p13 last updated on 11/Dec/19 $$\int\frac{\mathrm{1}}{{x}^{\mathrm{5}} −\mathrm{1}}{dx} \\ $$ Answered by MJS last updated on 11/Dec/19 $$\mathrm{decomposing} \\ $$$$\int\frac{{dx}}{{x}^{\mathrm{5}} −\mathrm{1}}={I}_{\mathrm{1}} +{I}_{\mathrm{2}}…
Question Number 75444 by vishalbhardwaj last updated on 11/Dec/19 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{b}/\mathrm{w}\:\mathrm{the}\:\mathrm{lines} \\ $$$$\mathrm{whose}\:\mathrm{direction}\:\mathrm{cosines}\:\mathrm{are}\:\mathrm{given} \\ $$$$\mathrm{by}\:\mathrm{the}\:\mathrm{equations}\:{l}\:+\:{m}\:+\:{n}\:=\:\mathrm{0} \\ $$$$,\:{l}^{\mathrm{2}} \:+\:{m}^{\mathrm{2}} \:−\:{n}^{\mathrm{2}} \:=\:\mathrm{0}\:?? \\ $$$$ \\ $$ Commented by…
Question Number 140982 by Mathspace last updated on 14/May/21 $${convergence}\:{and}\:{value}\:{of} \\ $$$$\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{{n}^{{n}} }{\left({n}!\right)^{\mathrm{2}} } \\ $$$$ \\ $$$$ \\ $$ Commented by mohammad17…
Question Number 75445 by vishalbhardwaj last updated on 11/Dec/19 $$\mathrm{If}\:\mathrm{a}\:\mathrm{variable}\:\mathrm{line}\:\mathrm{in}\:\mathrm{two}\:\mathrm{adjacent} \\ $$$$\mathrm{positions}\:\mathrm{has}\:\mathrm{direction}\:\mathrm{cosines} \\ $$$${l},{m},\:{n}\:\mathrm{and}\:{l}+\delta{l},\:{m}+\delta{m},\:{n}+\delta{n} \\ $$$$,\:\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{small}\:\mathrm{angle}\:\delta\theta\: \\ $$$$\mathrm{b}/\mathrm{w}\:\mathrm{the}\:\mathrm{two}\:\mathrm{positions}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by} \\ $$$$\delta\theta^{\mathrm{2}} \:=\:\delta{l}^{\mathrm{2}} \:+\:\delta{m}^{\mathrm{2}} \:+\:\delta{n}^{\mathrm{2}} \:\:?? \\…
Question Number 9908 by ridwan balatif last updated on 15/Jan/17 Commented by ridwan balatif last updated on 15/Jan/17 $$\:\mathrm{x}\:\mathrm{maximum}\:=…? \\ $$ Answered by mrW1 last…
Question Number 140977 by Mathspace last updated on 14/May/21 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{e}^{−{t}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)} }{\mathrm{1}+{x}^{\mathrm{2}} }{dx}\:\:{with}\:{t}\geqslant\mathrm{0} \\ $$ Answered by mathmax by abdo last updated on…
Question Number 9907 by amir last updated on 15/Jan/17 Commented by RasheedSoomro last updated on 15/Jan/17 $$\mathrm{What}\:\mathrm{is}\:\mathrm{meant}\:\mathrm{by}\:\mathrm{h}_{{a}} ? \\ $$ Commented by amir last updated…
Question Number 140976 by Mathspace last updated on 14/May/21 $${find}\:\int_{\mathrm{0}} ^{\pi} \:\frac{{dx}}{\left(\mathrm{2}−{cosx}−{sinx}\right)^{\mathrm{2}} } \\ $$$$ \\ $$ Answered by Ar Brandon last updated on 14/May/21…
Question Number 75440 by aliesam last updated on 11/Dec/19 Commented by MJS last updated on 11/Dec/19 $$\mathrm{I}'\mathrm{m}\:\mathrm{not}\:\mathrm{good}\:\mathrm{at}\:\mathrm{this}\:\mathrm{but}\:\mathrm{it}\:\mathrm{should}\:\mathrm{be}\:\mathrm{true} \\ $$$$\mathrm{for}\:\mathrm{any}\:{x}\:\mathrm{at}\:\mathrm{least}\:{x}\geqslant\mathrm{1} \\ $$$$\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{k}} \mathrm{e}^{−\left(\mathrm{2}{k}−\mathrm{1}\right){x}} }{\left(\mathrm{2}{k}−\mathrm{1}\right)\left(\mathrm{1}−\mathrm{e}^{−\mathrm{2}{x}}…