Question Number 66105 by Rio Michael last updated on 09/Aug/19 $${Find}\:\:\int_{−\mathrm{1}} ^{\mathrm{1}} \frac{\mathrm{9}\:+\mathrm{4}{x}^{\mathrm{2}} }{\mathrm{9}−\mathrm{4}{x}^{\mathrm{2}} }\:{dx} \\ $$ Commented by Prithwish sen last updated on 09/Aug/19…
Question Number 66103 by Rio Michael last updated on 09/Aug/19 $${A}\:{binary}\:{relation}\:{R}\:{is}\:{defined}\:{on}\:\mathbb{N},{the}\:{set}\:{of}\:{natural}\:{numbers}\:{by}\: \\ $$$$\:_{{x}} {R}_{{y}} \:\Leftrightarrow\:\exists\:{n}\:\in\:\mathbb{Z}\::\:{x}\:=\:\mathrm{2}^{{n}} {y},\:\:{x},{y}\:\in\:\mathbb{N} \\ $$$${show}\:{that}\:{R}\:{is}\:{an}\:{equivalence}\:{relation} \\ $$ Commented by Prithwish sen last…
Question Number 66102 by Rio Michael last updated on 09/Aug/19 $${prove}\:{by}\:{mathematical}\:{induction}\:{that}\:\:\mathrm{4}^{{n}} +\mathrm{3}^{{n}} +\mathrm{2}\:{is}\:{a}\:{multiple}\:{of}\:\mathrm{3}\:{for}\:{all}\: \\ $$$${positive}\:{integral}\:{values}\:{of}\:{n}. \\ $$ Commented by mathmax by abdo last updated on…
Question Number 66101 by Rio Michael last updated on 09/Aug/19 $${find}\:\frac{{dy}}{{dx}}\:\:{when}\:{y}\:=\:{x}^{\mathrm{2}} {ln}\left(\mathrm{3}{x}\right) \\ $$$${Given}\:{that}\:{xsinx}\:−\:{y}^{\mathrm{2}} =\mathrm{0}\:{show}\:{that}\:\:{y}^{\mathrm{2}} \:=\:\mathrm{2}{cosx}\:−\mathrm{2}\left(\frac{{dy}}{{dx}}\right)^{\mathrm{2}} \:−\mathrm{2}{y}\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} } \\ $$ Commented by Prithwish sen…
Question Number 66071 by AnjanDey last updated on 08/Aug/19 $$\mathrm{Evaluate}\:\mathrm{the}\:\mathrm{integral}\:\mathrm{as}\:\mathrm{a}\:\mathrm{limit}\:\mathrm{of}\:\mathrm{sums}: \\ $$$$\mathrm{1}.\int_{\mathrm{1}} ^{\mathrm{3}} \left({e}^{\mathrm{2}−\mathrm{3}{x}} +{x}^{\mathrm{2}} +\mathrm{1}\right){dx} \\ $$ Answered by meme last updated on 08/Aug/19…
Question Number 532 by 123456 last updated on 25/Jan/15 $${if}\:{f}\:{is}\:{continuos}\:{and}\:{diferentiable} \\ $$$${everywhere}\:{on}\:\mathbb{R},\:{if}\:{f}\left(\mathrm{0}\right)=\mathrm{0}\:{and} \\ $$$$\mid{f}'\left({x}\right)\mid\leqslant\mid{f}\left({x}\right)\mid\:{then}\:{proof}\:{that} \\ $$$${f}\left({x}\right)=\mathrm{0} \\ $$ Answered by prakash jain last updated on…
Question Number 66058 by arvinddayama01@gmail.comm last updated on 08/Aug/19 $${If}\:\:\:\:{x}\:+\:\frac{\mathrm{1}}{{x}}=\mathrm{1} \\ $$$$ \\ $$$${find}\:{out}\:{value}:− \\ $$$$ \\ $$$$\:\:\:\:\frac{{x}^{\mathrm{20}} +{x}^{\mathrm{17}} +{x}^{\mathrm{14}} +{x}^{\mathrm{11}} }{{x}^{\mathrm{17}} +{x}^{\mathrm{14}} +{x}^{\mathrm{11}} +{x}^{\mathrm{8}}…
Question Number 66061 by mathmax by abdo last updated on 08/Aug/19 $${let}\:{f}\left({t}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{sinx}}{\mathrm{1}+{te}^{−{x}^{\mathrm{2}} } }{dx}\:\:\:\:{with}\:\mid{t}\mid<\mathrm{1} \\ $$$${developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$ Terms of Service Privacy Policy…
Question Number 131580 by Dwaipayan Shikari last updated on 06/Feb/21 $$\boldsymbol{\mathrm{Prove}}\:\boldsymbol{\mathrm{or}}\:\boldsymbol{\mathrm{disprove}} \\ $$$$\underset{\boldsymbol{{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\boldsymbol{{n}}^{\mathrm{2}} +\mathrm{97}\right)^{\mathrm{2}} }=\frac{\boldsymbol{\pi}^{\mathrm{2}} }{\mathrm{97}\left(\boldsymbol{{e}}^{\boldsymbol{\pi}\sqrt{\mathrm{97}}} −{e}^{−\boldsymbol{\pi}\sqrt{\mathrm{97}}} \right)^{\mathrm{2}} }+\frac{\boldsymbol{\pi}}{\mathrm{388}}.\frac{{e}^{\mathrm{2}\boldsymbol{\pi}\sqrt{\mathrm{97}}} +\mathrm{1}}{\boldsymbol{{e}}^{\mathrm{2}\boldsymbol{\pi}\sqrt{\mathrm{97}}} −\mathrm{1}}+\frac{\mathrm{37635}}{\mathrm{37636}}−\frac{\mathrm{1}}{\:\mathrm{388}\sqrt{\mathrm{97}}} \\ $$…
Question Number 66018 by Rio Michael last updated on 07/Aug/19 $${prove}\:{by}\:{mathematical}\:{induction}\:{that}\: \\ $$$$\:\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}{r}\left({r}\:+\:\mathrm{1}\right)\:=\:\frac{{n}}{\mathrm{3}}\left({n}\:+\:\mathrm{1}\right)\left({n}\:+\:\mathrm{2}\right) \\ $$ Commented by Prithwish sen last updated on 07/Aug/19…