Question Number 77759 by abdomathmax last updated on 09/Jan/20 $${calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}}{{n}^{\mathrm{2}} \:+\mathrm{1}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 77754 by abdomathmax last updated on 09/Jan/20 $${U}_{{n}} {isa}\:{sequence}\:{woch}\:{verify} \\ $$$${U}_{{n}} +{U}_{{n}+\mathrm{1}} ={n}^{\mathrm{2}} \left(−\mathrm{1}\right)^{{n}} \:\:\forall\:{n}\geqslant\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{detdrmine}\:{U}_{{n}} \:{interm}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{nsture}\:{of}\:{the}\:{serie}\:\Sigma\:\frac{{U}_{{n}} }{{n}^{\mathrm{4}} } \\…
Question Number 143260 by Mathspace last updated on 12/Jun/21 $${find}\:\int\:\frac{{dx}}{\:\sqrt{{x}}+\sqrt{{x}+\mathrm{1}}+\sqrt{{x}+\mathrm{2}}} \\ $$ Commented by MJS_new last updated on 12/Jun/21 $$\mathrm{there}\:\mathrm{exists}\:\mathrm{a}\:\mathrm{solution}\:\mathrm{on}\:\mathrm{this}\:\mathrm{forum},\:\mathrm{I}\:\mathrm{cannot} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{question}\:\mathrm{number}… \\ $$ Terms…
Question Number 143261 by Mathspace last updated on 12/Jun/21 $${find}\:{Y}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)….\left({x}+{n}\right)} \\ $$$$\left({n}>\mathrm{1}\:{integr}\right) \\ $$ Answered by Olaf_Thorendsen last updated on 12/Jun/21 $$…
Question Number 143262 by Mathspace last updated on 12/Jun/21 $${developp}\:{at}\:{fourier}\:{serie} \\ $$$${f}\left({x}\right)=\frac{\mathrm{1}}{{cosx}\:+\mathrm{2}{sinx}} \\ $$ Answered by mathmax by abdo last updated on 13/Jun/21 $$\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\mathrm{cosx}+\mathrm{2sinx}}\:\Rightarrow\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\frac{\mathrm{e}^{\mathrm{ix}} +\mathrm{e}^{−\mathrm{ix}}…
Question Number 143256 by Mathspace last updated on 12/Jun/21 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \int_{{x}} ^{\mathrm{2}−{x}} {e}^{−{xy}} \sqrt{{x}+{y}}{dy}\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 143257 by Mathspace last updated on 12/Jun/21 $${find}\:\int\int_{\left[\mathrm{0},\mathrm{1}\right]} {e}^{−\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)} {arctan}\left(\mathrm{2}\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\right){dxdy} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 143259 by Mathspace last updated on 12/Jun/21 $${solve}\:{y}^{''} −{y}^{'} +\mathrm{2}={xsin}\left(\mathrm{3}{x}\right) \\ $$ Answered by qaz last updated on 12/Jun/21 $$\mathrm{y}_{\mathrm{p}} =\frac{\mathrm{1}}{\mathrm{D}^{\mathrm{2}} −\mathrm{D}}\left[\mathrm{xsin}\:\left(\mathrm{3x}\right)−\mathrm{2}\right] \\…
Question Number 143258 by Mathspace last updated on 12/Jun/21 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{1}} \int_{{x}} ^{{x}^{\mathrm{2}} } \:\frac{{sh}\left({xt}\right)}{{x}+{t}}{dt} \\ $$ Answered by Mathspace last updated on 13/Jun/21 $$\int_{{x}} ^{{x}^{\mathrm{2}}…
Question Number 143255 by Mathspace last updated on 12/Jun/21 $${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \frac{{sin}\left(\mathrm{1}−{cosx}\right)+\mathrm{1}−{cos}\left({sinx}\right)}{{x}^{\mathrm{2}} } \\ $$ Answered by bramlexs22 last updated on 12/Jun/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\frac{\mathrm{sin}\:\left(\mathrm{1}−\mathrm{cos}\:{x}\right)}{\mathrm{1}−\mathrm{cos}\:{x}}.\left(\mathrm{1}−\mathrm{cos}\:{x}\right)+\mathrm{1}−\mathrm{cos}\:\left(\mathrm{sin}\:{x}\right)}{{x}^{\mathrm{2}} } \\…