Question Number 67010 by mathmax by abdo last updated on 21/Aug/19 $${calculate}\:\:\sum_{{n}=\mathrm{4}} ^{+\infty} \:\:\:\:\frac{{n}}{\left({n}^{\mathrm{2}} −\mathrm{9}\right)^{\mathrm{2}} } \\ $$ Commented by mathmax by abdo last updated…
Question Number 67011 by mathmax by abdo last updated on 21/Aug/19 $${calculate}\:{U}_{{n}} =\int_{\mathrm{1}} ^{+\infty} \:\:\frac{{arctan}\left({n}\left[{x}\right]\right)}{{x}^{\mathrm{2}} }{dx} \\ $$ Commented by mathmax by abdo last updated…
Question Number 67008 by mathmax by abdo last updated on 21/Aug/19 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dt}}{\left({x}^{\mathrm{2}} \:+{t}^{\mathrm{2}} \right)^{\mathrm{2}} }\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:\left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{also}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dt}}{\left({x}^{\mathrm{2}} \:+{t}^{\mathrm{2}} \right)^{\mathrm{3}}…
Question Number 1472 by 123456 last updated on 11/Aug/15 $$\mathrm{find}\:{f}:\left[\mathrm{0},\mathrm{1}\right]\rightarrow\mathbb{R}\:\mathrm{such}\:\mathrm{that} \\ $$$${a}.\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{fdt}=\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\sqrt{\mathrm{1}+\left(\frac{{df}}{{dt}}\right)^{\mathrm{2}} }{dt} \\ $$$${b}.\forall{x}\in\left[\mathrm{0},\mathrm{1}\right] \\ $$$$\underset{\mathrm{0}} {\overset{{x}} {\int}}{fdt}=\underset{\mathrm{0}} {\overset{{x}} {\int}}\sqrt{\mathrm{1}+\left(\frac{{df}}{{dt}}\right)^{\mathrm{2}}…
Question Number 67006 by mathmax by abdo last updated on 21/Aug/19 $${calculae}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{{n}} }\:\:\:{with}\:{n}\:{integr}\:{natural}\:{and}\:{n}>\mathrm{0} \\ $$ Commented by mathmax by abdo last…
Question Number 67004 by sandeepkeshari0797@gmail.com last updated on 21/Aug/19 Answered by $@ty@m123 last updated on 21/Aug/19 $${Its}\:{repeatation}\:{of}\:{Q}.\:{No}.\:\mathrm{66356}. \\ $$$${Already}\:{answered}. \\ $$ Commented by sandeepkeshari0797@gmail.com last…
Question Number 67005 by mathmax by abdo last updated on 21/Aug/19 $${find}\:\int\:\:\:\frac{{x}−\mathrm{2}\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{{x}+\mathrm{2}\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{dx} \\ $$ Commented by mathmax by abdo last updated on 27/Aug/19…
Question Number 1468 by havandip last updated on 11/Aug/15 $$ \\ $$ Answered by 123456 last updated on 11/Aug/15 $$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:{f}\left({x}\right)=\mathrm{L} \\ $$$$\forall\epsilon>\mathrm{0},\exists\mathrm{M}\in\mathbb{R},\forall{x}<\mathrm{M},\mid{f}\left({x}\right)−\mathrm{L}\mid<\epsilon \\ $$…
Question Number 132537 by SLVR last updated on 15/Feb/21 $${If}\:{f}\left({x}\right)=\mathrm{8}{x}^{\mathrm{3}\:} +\mathrm{3}{x}\:{then}\:{lim}_{{x}\rightarrow\infty} \frac{{x}^{\mathrm{1}/\mathrm{3}} }{{f}^{−\mathrm{1}} \left(\mathrm{8}{x}\right)−{f}^{−\mathrm{1}} \left({x}\right)}\:{is} \\ $$ Commented by SLVR last updated on 15/Feb/21 $${can}\:{any}\:{one}\:{help}\:{me}…{please}…
Question Number 1466 by Rasheed Soomro last updated on 10/Aug/15 $${Without}\:{using}\:{calculus}\:{find}\:{stepwise}\:{solution}: \\ $$$$\underset{{x}\rightarrow−\propto} {{lim}}\:\frac{{a}^{{x}} −\mathrm{1}}{{x}}\:{where}\:{a}>\mathrm{1} \\ $$ Answered by 123456 last updated on 11/Aug/15 $${a}>\mathrm{1},{x}<\mathrm{0}\Rightarrow{a}^{{x}}…