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…
Question Number 66016 by Rio Michael last updated on 07/Aug/19 $${Evaluate}\:\:\: \\ $$$${a}.\:\int_{\mathrm{1}} ^{\mathrm{2}} \:\left({lnx}\right)^{\mathrm{2}} {dx} \\ $$$${b}.\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{6}}} \:{sin}^{\mathrm{2}} {x}\:{cos}^{\mathrm{3}} {xdx} \\ $$ Commented…
Question Number 66019 by Rio Michael last updated on 07/Aug/19 $$\underset{{x}\rightarrow\infty} {{lim}}\:\left(\mathrm{1}\:+\:\frac{\mathrm{2}}{{x}}\right)^{{x}} \:= \\ $$ Commented by mathmax by abdo last updated on 07/Aug/19 $${let}\:{f}\left({x}\right)=\left(\mathrm{1}+\frac{\mathrm{2}}{{x}}\right)^{{x}}…
Question Number 481 by 123456 last updated on 12/Jan/15 $${proof}\:{or}\:{given}\:{a}\:{counter}\:{example}: \\ $$$${if}\:\left\{{x}_{{n}} \right\}\:{is}\:{a}\:{no}\:{limited}\:{sequence} \\ $$$${then} \\ $$$${exist}\:{a}\:{sub}−{sequence}\:\left\{{x}_{{nk}} \right\}\:{that} \\ $$$$\underset{{n}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}}{{x}_{{nk}} }=\mathrm{0} \\ $$ Commented…
Question Number 66017 by Rio Michael last updated on 07/Aug/19 $${show}\:{that}\:{the}\:{equation}\:{xe}^{{x}} =\mathrm{1}\:{has}\:{a}\:{root}\:{between}\:\mathrm{0}.\mathrm{5}\:{and}\:\mathrm{0}.\mathrm{6}\:{starting} \\ $$$${with}\:\mathrm{0}.\mathrm{55}\:{as}\:{a}\:{first}\:{approximate}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 476 by 123456 last updated on 11/Jan/15 $${given}\:{a}_{{n}} \:{and}\:{b}_{{n}} \:{two}\:{real}\:{sequence} \\ $$$${can}\:{a}\:{serie}\:\underset{{n}=\mathrm{1}} {\overset{+\infty} {\sum}}{a}_{{n}} \:{and}\:\underset{{n}=\mathrm{1}} {\overset{+\infty} {\sum}}{b}_{{n}} \:{diverge} \\ $$$${but} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{+\infty}…