Question Number 128030 by Agnibhoo last updated on 03/Jan/21 $$\:\mathrm{99}\:×\:\mathrm{99}\:=\:\mathrm{9801} \\ $$$$\:\mathrm{999}\:×\:\mathrm{999}\:=\:\mathrm{998001} \\ $$$$\:\mathrm{9999}\:×\:\mathrm{9999}\:=\:\mathrm{99980001} \\ $$$$\:\mathrm{99999}\:×\:\mathrm{99999}\:=\:? \\ $$$$\:\mathrm{999999}\:×\:\mathrm{999999}\:=\:? \\ $$ Answered by Geovanek last updated…
Question Number 128008 by AgnibhoMukhopadhyay last updated on 03/Jan/21 $$\mathrm{If}\:\mathrm{347}.\mathrm{9823}\:=\:\frac{\mathrm{3}}{{P}}\:+\:\mathrm{4}{Q}\:+\:\mathrm{7}{R}\:+\:\frac{\mathrm{9}}{\mathrm{10}}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+\:\frac{\mathrm{8}}{\mathrm{100}}\:+\:\frac{\mathrm{2}}{{S}}\:+\:\frac{\mathrm{3}}{{T}} \\ $$$${Then}\:{find}\:{the}\:{value}\:{of}\: \\ $$$${P}\:+\:{Q}\:+\:{R}\:+\:{S}\:+\:{T} \\ $$ Answered by MJS_new last updated on 03/Jan/21…
Question Number 128001 by Agnibhoo last updated on 03/Jan/21 $$\left(\mathrm{x}\:−\:\mathrm{a}\right)\:\left(\mathrm{x}\:−\:\mathrm{b}\right)\:\left(\mathrm{x}\:−\:\mathrm{c}\right)\:…..\:\left(\mathrm{x}\:−\:\mathrm{z}\right)\:=\:? \\ $$ Answered by prakash1956 last updated on 03/Jan/21 $$\left(\mathrm{x}\:−\:\mathrm{a}\right)\:\left(\mathrm{x}\:−\:\mathrm{b}\right)\:\left(\mathrm{x}\:−\:\mathrm{c}\right)\:…..\:\left(\mathrm{x}\:−\:\mathrm{z}\right)\:=\:? \\ $$$$=\mathrm{0}\:\:\:\left(\mathrm{x}−\mathrm{x}\right)\:\mathrm{term}\:\mathrm{involved}\:\mathrm{in}\:\mathrm{this} \\ $$$$ \\…
Question Number 127982 by Dwaipayan Shikari last updated on 03/Jan/21 $${Some}\:{Values}\:.. \\ $$$$\underset{{n}=−\infty} {\overset{\infty} {\sum}}{e}^{−\pi{n}^{\mathrm{2}} } =\frac{\pi^{\frac{\mathrm{1}}{\mathrm{4}}} }{\Gamma\left(\frac{\mathrm{3}}{\mathrm{4}}\right)} \\ $$$$\underset{{n}=−\infty} {\overset{\infty} {\sum}}{e}^{−\mathrm{2}\pi{n}^{\mathrm{2}} } =\frac{\pi^{\frac{\mathrm{1}}{\mathrm{4}}} }{\Gamma\left(\frac{\mathrm{3}}{\mathrm{4}}\right)}\:\frac{\sqrt[{\mathrm{4}}]{\mathrm{6}+\mathrm{4}\sqrt{\mathrm{2}}}}{\mathrm{2}}…
Question Number 127974 by Dwaipayan Shikari last updated on 03/Jan/21 $$\overset{\bullet\bullet} {\theta}+\frac{{g}}{{l}}{sin}\theta=\mathrm{0} \\ $$$${Exact}\:{form}\:\left({May}\:{include}\:{elliptic}\:{integral}\right) \\ $$ Commented by Dwaipayan Shikari last updated on 03/Jan/21 $${My}\:{try}…
Question Number 127970 by Agnibhoo last updated on 03/Jan/21 $$\mathrm{You}\:\mathrm{have}\:\mathrm{given}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{integer}\:{N}.\: \\ $$$$\mathrm{Calculate}\: \\ $$$$\int_{\:\mathrm{0}} ^{\:\infty} \frac{{e}^{\mathrm{2}\pi{x}^{\mathrm{2}} } \:−\:\mathrm{1}}{{e}^{\mathrm{2}\pi{x}^{\mathrm{2}} } \:+\:\mathrm{1}}\left(\frac{\mathrm{1}}{{x}}\:−\:\frac{{x}}{{N}^{\mathrm{2}} \:−\:{x}^{\mathrm{2}} }\right)\:{dx} \\ $$ Answered…
Question Number 62413 by mathmax by abdo last updated on 20/Jun/19 $${calculate}\:\:{W}_{{n}} =\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{cos}^{{n}} {xdx}\:\:\:\left(\:{n}\:{from}\:{N}\right)\:{and}\:{J}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{sin}^{{n}} {xdx} \\ $$ Terms of Service…
Question Number 62410 by mathmax by abdo last updated on 20/Jun/19 $$\:\:{prove}\:{that}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{t}} {ln}\left({t}\right)\:{dt}\:=−\gamma\:\:\:\:\:\:\:\left(\:\:\gamma\:{is}\:{the}\:{constant}\:{of}\:{euler}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 127933 by AgnibhoMukhopadhyay last updated on 03/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{\frac{\mathrm{1}}{{x}\:−\:\mathrm{3}}\:+\:\frac{\mathrm{1}}{{x}\:+\:\mathrm{4}}} \\ $$$$ \\ $$$$\mathrm{If}\:{x}\:>\:\mathrm{0}\:\mathrm{and}\:{x}\:\neq\:\mathrm{3},\:\mathrm{which}\:\mathrm{of}\:\mathrm{the}\:\:\: \\ $$$$\mathrm{following}\:\mathrm{is}\:\mathrm{equivalent}\:\mathrm{to}\:\mathrm{the}\: \\ $$$$\mathrm{expresion}\:\mathrm{above}? \\ $$$$\mathrm{A}.\:\:\mathrm{2}{x}\:+\:\mathrm{1} \\ $$$$\mathrm{B}.\:\:{x}^{\mathrm{2}} \:+\:{x}\:−\:\mathrm{12}\: \\ $$$$\mathrm{C}.\:\:\frac{{x}^{\mathrm{2}}…
Question Number 62395 by Cypher1207 last updated on 20/Jun/19 $$\mathrm{The}\:\mathrm{Most}\:\mathrm{Beautiful}\:\mathrm{Equation} \\ $$$$\mathrm{for}\:\mathrm{me}\:\mathrm{is}: \\ $$$$\mathrm{e}^{{i}\pi} +\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{INCREDIBLE}! \\ $$$$#\mathrm{Euler}'\mathrm{sIdentity} \\ $$ Commented by JDamian last…