Question Number 124066 by Bird last updated on 30/Nov/20 $${let}\:{f}\left({x}\right)={arctan}\left(\frac{\mathrm{2}}{{x}}\right) \\ $$$${calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{1}\right) \\ $$$${find}\:{f}^{\left(\mathrm{7}\right)} \left(\frac{\mathrm{1}}{\mathrm{7}}\right) \\ $$ Answered by Olaf last updated on…
Question Number 124065 by Bird last updated on 30/Nov/20 $${determine}\:{tbe}\:{sewuence}\:{u}_{{n}} \\ $$$${wich}\:{verify}\:{u}_{{n}} +{u}_{{n}+\mathrm{1}} =\frac{\left(−\mathrm{1}\right)^{{n}} }{\:\sqrt{{n}}} \\ $$$${n}>\mathrm{0} \\ $$ Answered by mindispower last updated on…
Question Number 58354 by maxmathsup by imad last updated on 21/Apr/19 $${let}\:{U}_{{n}} =\frac{\mathrm{1}^{\mathrm{2}} \:+\mathrm{2}^{\mathrm{2}} \:+\mathrm{3}^{\mathrm{2}} \:+….+{n}^{\mathrm{2}} }{\mathrm{1}^{\mathrm{4}} \:+\mathrm{2}^{\mathrm{4}} \:+\mathrm{3}^{\mathrm{4}} \:+….+{n}^{\mathrm{4}} } \\ $$$$\left.\mathrm{1}\right){find}\:{lim}_{{n}\rightarrow+\infty} {U}_{{n}} \\…
Question Number 123706 by I want to learn more last updated on 27/Nov/20 $$\mathrm{If}\:\:\:\:\mathrm{h}\left(\mathrm{x}\right)\:\:=\:\:\mathrm{f}^{\mathrm{2}} \left(\mathrm{x}\right)\:\:−\:\:\mathrm{g}^{\mathrm{2}} \left(\mathrm{x}\right),\:\:\:\:\:\:\:\:\mathrm{f}\:'\left(\mathrm{x}\right)\:\:\:=\:\:\:−\:\mathrm{g}\left(\mathrm{x}\right)\:\:\:\:\mathrm{and}\:\:\:\:\:\mathrm{g}\:'\left(\mathrm{x}\right)\:\:=\:\:\mathrm{f}\left(\mathrm{x}\right) \\ $$$$\:\:\:\mathrm{then}\:\:\:\:\mathrm{h}\:'\left(\mathrm{x}\right)\:\:=\:\:\:??? \\ $$$$ \\ $$$$\left(\mathrm{a}\right)\:\:\:\:\mathrm{0}\:\:\:\:\:\:\:\:\:\left(\mathrm{b}\right)\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{c}\right)\:\:\:\:\:−\:\:\mathrm{4}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{g}\left(\mathrm{x}\right)\:\:\:\:\:\:\:\:\:\:\left(\mathrm{d}\right)\:\:\:\:\:\left[−\mathrm{g}\left(\mathrm{x}\right)\right]^{\mathrm{2}} \:\:−\:\:\left[\mathrm{f}\left(\mathrm{x}\right)\right]^{\mathrm{2}} \\ $$…
Question Number 123675 by mathmax by abdo last updated on 27/Nov/20 $$\mathrm{calculste}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \:\:\:\frac{\mathrm{arctan}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}\right)−\mathrm{arctan}\left(\mathrm{x}+\mathrm{1}\right)}{\mathrm{x}^{\mathrm{3}} } \\ $$ Answered by benjo_mathlover last updated on 27/Nov/20 $$\underset{{x}\rightarrow\mathrm{0}}…
Question Number 123672 by mathmax by abdo last updated on 27/Nov/20 $$\mathrm{find}\:\mathrm{nature}\:\mathrm{of}\:\mathrm{the}\:\mathrm{serie}\:\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \:\mathrm{cos}\left(\pi\sqrt{\mathrm{n}^{\mathrm{2}} +\mathrm{n}+\mathrm{1}}\right) \\ $$ Answered by mnjuly1970 last updated on 27/Nov/20 $$\sqrt{{n}^{\mathrm{2}}…
Question Number 58103 by smiak8742 last updated on 17/Apr/19 $${f}\left({x}\right)=−{x}^{\mathrm{6}} +\mathrm{3}\:{x}^{\mathrm{4}} \:+\:\mathrm{4}{x}^{\mathrm{2}} {find}\:{the}\:{zeros} \\ $$ Answered by MJS last updated on 17/Apr/19 $${x}^{\mathrm{6}} −\mathrm{3}{x}^{\mathrm{4}} −\mathrm{4}{x}^{\mathrm{2}}…
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Question Number 58079 by smiak8742 last updated on 17/Apr/19 $${f}\left({x}\right)=\mathrm{2}^{\mathrm{3}} +{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{2};{x}+\mathrm{2} \\ $$ Answered by $@ty@m last updated on 17/Apr/19 Terms of Service Privacy…
Question Number 123593 by Bird last updated on 26/Nov/20 $${solve}\:{y}^{''} \:+\mathrm{2}{y}^{'} \:−{y}={xe}^{−{x}^{\mathrm{2}} } \\ $$ Answered by mathmax by abdo last updated on 27/Nov/20 $$\mathrm{h}\rightarrow\mathrm{r}^{\mathrm{2}}…