Question Number 33257 by prof Abdo imad last updated on 14/Apr/18 $${let}\:{g}\left({x}\right)=\:\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{4}} } \\ $$$$\left.\mathrm{1}\right)\:{find}\:{g}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{g}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\:{if}\:{g}\left({x}\right)=\Sigma\:{u}_{{n}} \:{x}^{{n}} \:\:\:{find}\:{the}\:{sequence}\:{u}_{{n}} \\ $$…
0-x-1-ln-F-x-5-cos-pix-x-1-F-x-5-cos-pix-x-1-dx-F-x-Fib-x-xth-Extended-fibonacci-number-f-R-R-1-5-2-
Question Number 98776 by M±th+et+s last updated on 16/Jun/20 $$\int_{\mathrm{0}} ^{\infty} \frac{\left({x}−\mathrm{1}\right)}{{ln}\left({F}\left({x}\right)\sqrt{\mathrm{5}}+{cos}\left(\pi{x}\right)\left(\varphi\right)^{−{x}} −\mathrm{1}\right)\sqrt{{F}\left({x}\right)\sqrt{\mathrm{5}}+{cos}\left(\pi{x}\right)\left(\varphi\right)^{−{x}} −\mathrm{1}}}{dx} \\ $$$$ \\ $$$${F}\left({x}\right)={Fib}\left({x}\right)={xth}\:{Extended}\:{fibonacci}\:{number} \\ $$$${f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$$\varphi=\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$ Terms…
Question Number 33232 by prof Abdo imad last updated on 13/Apr/18 $${find}\:{the}\:{value}\:{of}\:\:\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{x}\:{sin}\left(\mathrm{2}{x}\right)}{\left(\mathrm{1}+\mathrm{4}{x}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dx}\:. \\ $$ Commented by prof Abdo imad last updated…
Question Number 33223 by prof Abdo imad last updated on 13/Apr/18 $${let}\:\:{A}_{{n}} \:=\int_{−\infty} ^{+\infty} \:\:\:\frac{{e}^{{i}\pi{x}} }{\mathrm{1}+{x}+{x}^{\mathrm{2}} \:+…{x}^{{n}−\mathrm{1}} }\:\:{with}\:{n}\geqslant\mathrm{3}\:{integr} \\ $$$${find}\:{the}\:{value}\:{of}\:{A}_{{n}} \:. \\ $$ Terms of…
Question Number 33222 by prof Abdo imad last updated on 13/Apr/18 $${let}\:{give}\:{n}\:\geqslant\mathrm{3}\:{integr}\:\:{calculate} \\ $$$${I}_{{n}} =\:\int_{−\infty} ^{+\infty} \:\:\:\:\:\frac{{dx}}{\mathrm{1}+{x}\:+{x}^{\mathrm{2}} \:+….+{x}^{{n}−\mathrm{1}} } \\ $$ Terms of Service Privacy…
Question Number 33210 by abdo imad last updated on 12/Apr/18 $${find}\:\:{lim}_{{x}\rightarrow+\infty} \:\:{x}\:{e}^{−{x}^{\mathrm{2}} } \:\:\:\underset{\mathrm{0}} {\int}^{{x}−\mathrm{1}} \:\:{e}^{{t}^{\mathrm{2}} } \:{dt} \\ $$ Terms of Service Privacy Policy…
Question Number 98744 by M±th+et+s last updated on 15/Jun/20 $$\int_{\mathrm{0}} ^{\pi} \int_{\mathrm{0}} ^{\mathrm{2}{sin}\theta} \left(\mathrm{1}+{rsin}\theta\right){r}\:{dr}\:{d}\theta \\ $$ Commented by bemath last updated on 16/Jun/20 $$=\:\underset{\mathrm{0}} {\overset{\pi}…
Question Number 33204 by prof Abdo imad last updated on 12/Apr/18 $${find}\:{the}\:{value}\:{of}\:\int_{−\infty} ^{+\infty} \:\:\:\:\frac{{cos}\left({ax}\right)}{\mathrm{1}+{x}+{x}^{\mathrm{2}} }\:{dx}. \\ $$ Commented by abdo imad last updated on 13/Apr/18…
Question Number 33202 by prof Abdo imad last updated on 12/Apr/18 $${find}\:{the}\:{value}\:{of}\:\:\int_{−\infty} ^{+\infty} \:\:\:\:\:\frac{{dt}}{\left(\mathrm{1}+{t}\:+{t}^{\mathrm{2}} \right)^{\mathrm{2}} }\:. \\ $$ Commented by prof Abdo imad last updated…
Question Number 98722 by mathmax by abdo last updated on 15/Jun/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{arctan}\left(\frac{\mathrm{3}}{\mathrm{x}}\right) \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calculste}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{1}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{seri}\:\mathrm{at}\:\mathrm{point}\:\mathrm{x}_{\mathrm{0}} =\mathrm{1} \\ $$ Answered by MWSuSon last…