Question Number 32735 by caravan msup abdo. last updated on 01/Apr/18 $${let}\:{give}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dt}}{\mathrm{1}+{t}^{{n}} } \\ $$$$\left.\mathrm{1}\right)\:{find}\:{l}={lim}_{{n}\rightarrow\infty} \:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right){give}\:{a}\:{equivalent}\:{of}\:{A}_{{n}} −{l} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{a}\:{equivalent}\:{of}\:{A}_{{n}} \\…
Question Number 32734 by caravan msup abdo. last updated on 01/Apr/18 $$\left.\mathrm{1}\right)\:{a}\geqslant\mathrm{0}\:\:{calculate}\:\int_{\mathrm{0}} ^{{a}} \:\frac{{n}^{\mathrm{2}} \:−{x}^{\mathrm{2}} }{\left({n}^{\mathrm{2}} \:+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx}\:{with} \\ $$$${n}\:{integr} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{n}^{\mathrm{2}}…
Question Number 32732 by caravan msup abdo. last updated on 31/Mar/18 $${give}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{\left({lnx}\right)^{{p}} }{\mathrm{1}−{x}}\:{dx}\:{at}\:{form}\:{of}\:{seriewith} \\ $$$${p}\geqslant\mathrm{2}\:. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 32723 by caravan msup abdo. last updated on 31/Mar/18 $${find}\:{lim}_{{n}\rightarrow+\infty} \:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{t}} \:{sin}^{{n}} {t}\:{dt}. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 32701 by caravan msup abdo. last updated on 31/Mar/18 $${let}\:{give}\:{f}\left({x}\right)=\:\frac{{x}}{\:\sqrt{{x}+\mathrm{1}}} \\ $$$$\left.\mathrm{1}\left.\right){calculate}\:{f}^{−\mathrm{1}} \left({x}\right)\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\left({f}^{−\mathrm{1}} \right)^{'} \left({x}\right)\:. \\ $$ Commented by Rio Mike…
Question Number 98189 by abdomathmax last updated on 12/Jun/20 $$\mathrm{let}\:\xi\left(\mathrm{x}\right)\:=\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{x}} } \\ $$$$\mathrm{calculate}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{1}^{+} } \:\:\:\left(\mathrm{x}−\mathrm{1}\right)\xi\left(\mathrm{x}\right) \\ $$ Answered by mathmax by abdo last…
Question Number 98188 by abdomathmax last updated on 12/Jun/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\frac{\mathrm{arctan}\left(\mathrm{2x}\right)}{\mathrm{x}+\mathrm{3}} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right)\:\mathrm{snd}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie} \\ $$ Answered by mathmax by abdo last updated…
Question Number 163720 by alcohol last updated on 09/Jan/22 $$\int_{\mathrm{2}} ^{\:\mathrm{4}} \frac{\sqrt{{ln}\left(\mathrm{9}−{x}\right)}}{\:\sqrt{{ln}\left(\mathrm{9}−{x}\right)}+\sqrt{{ln}\left(\mathrm{3}+{x}\right)}}\:{dx} \\ $$$$ \\ $$ Answered by Mathspace last updated on 09/Jan/22 $${x}=\mathrm{6}−{t}\:\Rightarrow{t}=\mathrm{6}−{x}\:\Rightarrow \\…
Question Number 98186 by abdomathmax last updated on 12/Jun/20 $$\mathrm{solve}\:\mathrm{xy}^{\left(\mathrm{3}\right)} \:+\mathrm{x}^{\mathrm{2}} \mathrm{y}^{\left(\mathrm{2}\right)} \:+\mathrm{x}^{\mathrm{3}} \mathrm{y}^{\left(\mathrm{1}\right)} \:+\mathrm{x}^{\mathrm{4}} \mathrm{y}\:=\mathrm{e}^{−\mathrm{2x}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 98187 by abdomathmax last updated on 12/Jun/20 $$\mathrm{find}\:\mathrm{arctan}\left(\mathrm{x}\right)+\mathrm{arctany}\:\:\mathrm{at}\:\mathrm{form}\:\mathrm{of}\:\mathrm{arctan} \\ $$ Answered by Rio Michael last updated on 12/Jun/20 $$\mathrm{let}\:\mathrm{arctan}\:{x}\:=\:{u}\:\Rightarrow\:{x}\:=\:\mathrm{tan}\:{u} \\ $$$$\mathrm{and}\:\mathrm{let}\:\mathrm{tan}\:{y}\:=\:{v}\:\Rightarrow\:{y}\:=\:\mathrm{tan}\:{v} \\ $$$$\mathrm{suppose}\:\mathrm{arctan}\:{x}\:+\:\mathrm{arctan}\:{y}\:=\:\theta…