Question Number 26576 by gunawan last updated on 27/Dec/17 $$\mathrm{Find}\:\mathrm{all}\:{f}\::\:\mathrm{R}\rightarrow\mathrm{R}\:\mathrm{such}\:\mathrm{that} \\ $$$${f}\left({x}+{f}\left({x}\right)+{f}\left({y}\right)\right)={f}\left({y}+{f}\left({x}\right)\right)+{x}+{f}\left({y}\right)−{f}\left({f}\left({y}\right)\right)\: \\ $$$$\mathrm{for}\:\mathrm{all}\:{x},\:\mathrm{y}\:\in\:\mathrm{R} \\ $$ Commented by prakash jain last updated on 27/Dec/17 $${f}\left({x}+{f}\left({x}\right)+{f}\left({y}\right)\right)={f}\left({y}+{f}\left({x}\right)+{x}+{f}\left({y}\right)−{f}\left({f}\left({y}\right)\right)\right)?\:…
Question Number 26574 by abdo imad last updated on 26/Dec/17 $${study}\:{the}\:{nature}\:{of}\:{the}\:{serie}\:\:\:\sum_{{n}=\mathrm{2}} ^{\propto} \:\:\frac{{cosn}}{\:\sqrt{{n}+\left(−\mathrm{1}\right)^{{n}} }}\:{z}^{{n}} \\ $$ Commented by abdo imad last updated on 29/Dec/17 $${we}\:{have}\:\:\:\frac{\mathrm{1}}{\:\sqrt{{n}+\left(−\mathrm{1}\right)^{{n}}…
Question Number 26571 by abdo imad last updated on 26/Dec/17 $${let}\:{give}\:\:{I}\left({x}\right)=\:\:\int_{\mathrm{1}} ^{\propto} \:\frac{{t}−{E}\left({t}\right)}{{t}^{{x}+\mathrm{1}} }{dt}\:\:\:{prove}\:{that} \\ $$$$\xi\left({x}\right)=\:\frac{{x}}{{x}−\mathrm{1}}\:−{xI}\left({x}\right)\:{then}\:{chow}\:{that}\:\left({x}−\mathrm{1}\right)_{{x}−\mathrm{1}^{+\:{ew}} } \xi\left({x}\right)−−>\mathrm{1} \\ $$$${we}\:{remind}\:\:\xi\left({x}\right)\:=\:\sum_{{n}\geqslant\mathrm{1}} \:\frac{\mathrm{1}}{{n}^{{x}} }\:\:\:{and}\:\:{x}>\mathrm{1} \\ $$ Commented…
f-and-g-are-two-continous-function-on-R-find-we-suppose-f-and-g-odd-determine-lim-x-0-gof-x-fog-x-x-
Question Number 92086 by mathmax by abdo last updated on 04/May/20 $${f}\:{and}\:{g}\:{are}\:{two}\:{continous}\:{function}\:{on}\:{R}\:{find} \\ $$$${we}\:{suppose}\:{f}\:{and}\:{g}\:{odd}\:\:{determine}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\frac{{gof}\left({x}\right)−{fog}\left({x}\right)}{{x}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 92080 by mathmax by abdo last updated on 04/May/20 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\frac{{sin}\left(\mathrm{2}{shx}\right)\:−{sh}\left(\mathrm{2}{sinx}\right)}{{e}^{{x}} −\mathrm{1}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 92079 by mathmax by abdo last updated on 04/May/20 $${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \frac{{e}^{{sin}^{\mathrm{2}} {x}} −{e}^{{x}^{\mathrm{3}} −\mathrm{2}{x}} }{{x}^{\mathrm{2}} } \\ $$ Commented by john santu last…
Question Number 26400 by abdo imad last updated on 25/Dec/17 $${find}\:{the}\:{sequence}\:\left({u}_{{n}} \right)\:{wich}\:{verify}\:{u}_{{n}} \:−\mathrm{2}\:{u}_{{n}−\mathrm{1}} \:+\mathrm{1}=\:\mathrm{2}^{{n}} \\ $$ Answered by prakash jain last updated on 25/Dec/17 $${x}−\mathrm{2}=\mathrm{0}…
Question Number 26313 by Tinkutara last updated on 24/Dec/17 $$\mathrm{If}\:\mathrm{domain}\:\mathrm{of}\:{y}\:=\:{f}\left({x}\right)\:\mathrm{is}\:\left[−\mathrm{3},\:\mathrm{2}\right]\:\mathrm{and} \\ $$$${g}\left({x}\right)\:=\:{f}\left(\mid\left[{x}\right]\mid\right)\:\left(\left[\centerdot\right]\:\mathrm{denotes}\:\mathrm{the}\:\mathrm{greatest}\right. \\ $$$$\left.\mathrm{integer}\:\mathrm{function}\right),\:\mathrm{then}\:\mathrm{domain}\:\mathrm{of}\:{g}\left({x}\right) \\ $$$$\mathrm{is} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 26111 by abdo imad last updated on 19/Dec/17 $${find}\:\:{the}\:{radius}\:{of}\:{convergence}\:{for}\:{the}\:{serie}\:\:\:\sum_{{n}=\mathrm{1}} ^{\propto} \:{H}_{{n}} \:{x}^{{n}} \\ $$$${H}_{{n}} \:\:=\:\:\:\sum_{{k}=\mathrm{1}} ^{{k}={n}} \:\:\frac{\mathrm{1}}{{k}}\:. \\ $$ Commented by prakash jain…
Question Number 91640 by mathmax by abdo last updated on 02/May/20 $${find}\:{nature}\:{of}\:{the}\:{serie}\:\sum_{{n}} \:{cos}\left(\pi{n}^{\mathrm{2}} {ln}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)\right) \\ $$ Commented by mathmax by abdo last updated on 04/May/20…