Category: Relation and Functions

Question Number 17093 by 1234Hello last updated on 02/Jul/17 $$\mathrm{If}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{polynomial}\:\mathrm{function} \\ $$$$\mathrm{satisfying}\:{f}\left({x}\right).{f}\left(\frac{\mathrm{1}}{{x}}\right)\:=\:{f}\left({x}\right)\:+\:{f}\left(\frac{\mathrm{1}}{{x}}\right)\:; \\ $$$${x}\:\in\:{R}\:−\:\left\{\mathrm{0}\right\}\:\mathrm{and}\:{f}\left(\mathrm{3}\right)\:=\:\mathrm{28},\:\mathrm{then}\:{f}\left(\mathrm{4}\right)\:\mathrm{is} \\ $$$$\mathrm{equal}\:\mathrm{to} \\ $$ Commented by prakash jain last updated on…

Question Number 82452 by mathmax by abdo last updated on 21/Feb/20 $${nature}\:{ofthe}\:{serie}\:\sum_{{n}=\mathrm{0}} ^{\infty} {ln}\left({cos}\left(\frac{\mathrm{1}}{\mathrm{2}^{{n}} }\right)\right) \\ $$ Commented by mathmax by abdo last updated on…

Question Number 82445 by mathmax by abdo last updated on 21/Feb/20 $${calculate}\:\sum_{{n}=\mathrm{2}} ^{\infty} \:\frac{\xi\left({n}\right)−\mathrm{1}}{{n}} \\ $$$${with}\:\xi\left({x}\right)\:=\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{{n}^{{x}} }\:\:\:\left({x}>\mathrm{1}\right) \\ $$ Answered by mind is…

Question Number 147971 by mathmax by abdo last updated on 24/Jul/21 $$\mathrm{find}\:\int_{−\infty} ^{+\infty} \:\frac{\mathrm{x}^{\mathrm{3}} \mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}\right)^{\mathrm{4}} } \\ $$ Commented by tabata last updated on…

Question Number 147863 by mathmax by abdo last updated on 24/Jul/21 $$\mathrm{calculate}\:\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \:\frac{\mathrm{n}!^{\mathrm{2}} }{\left(\mathrm{2n}\right)!} \\ $$$$ \\ $$ Answered by qaz last updated on…