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Category: Relation and Functions

developp-at-integr-serie-f-x-1-x-1-x-2-

Question Number 94337 by mathmax by abdo last updated on 18/May/20 $${developp}\:{at}\:{integr}\:{serie}\:{f}\left({x}\right)\:=\frac{\mathrm{1}}{\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)} \\ $$ Answered by Rio Michael last updated on 18/May/20 $$\mathrm{if}\:\mathrm{you}\:\mathrm{mean}\:\mathrm{develope}\:\mathrm{a}\:\mathrm{series}\:\mathrm{then}: \\ $$$${f}\left({x}\right)\:=\:\frac{\mathrm{1}}{\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)}\:\equiv\:\frac{\mathrm{1}}{{x}−\mathrm{2}}\:−\frac{\mathrm{1}}{{x}−\mathrm{1}}…

let-f-x-sinx-x-if-x-0-and-f-0-1-1-findf-n-x-and-f-n-0-2-developp-f-at-integr-serie-st-x-0-0-and-x-0-pi-2-

Question Number 94334 by mathmax by abdo last updated on 18/May/20 $${let}\:{f}\left({x}\right)\:=\frac{{sinx}}{{x}}{if}\:{x}\neq\mathrm{0}\:\:{and}\:{f}\left(\mathrm{0}\right)=\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{findf}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right){developp}\:{f}\:{at}\:{integr}\:{serie}\:{st}\:{x}_{\mathrm{0}} =\mathrm{0}\:{and}\:{x}_{\mathrm{0}} =\frac{\pi}{\mathrm{2}} \\ $$ Answered by abdomathmax…

1-calculate-n-0-x-n-4n-2-1-with-x-lt-1-2-find-the-value-of-n-0-1-4n-2-1-and-n-0-1-n-4n-2-1-

Question Number 94331 by mathmax by abdo last updated on 18/May/20 $$\left.\mathrm{1}\right)\:{calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{{x}^{{n}} }{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}}\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}}{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}}\:{and}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}}…

Given-f-xy-f-x-y-and-f-7-7-find-f-1008-

Question Number 94318 by john santu last updated on 18/May/20 $$\mathrm{Given}\:\mathrm{f}\left(\mathrm{xy}\right)\:=\:\mathrm{f}\left(\mathrm{x}+\mathrm{y}\right)\:\mathrm{and}\: \\ $$$$\mathrm{f}\left(\mathrm{7}\right)\:=\:\mathrm{7}.\:\mathrm{find}\:\mathrm{f}\left(\mathrm{1008}\right)\: \\ $$ Commented by Rasheed.Sindhi last updated on 18/May/20 $${f}\left(\mathrm{7}\right)={f}\left(\mathrm{7}×\mathrm{1}\right)={f}\left(\mathrm{7}+\mathrm{1}\right)=\mathrm{7} \\ $$$${f}\left(\mathrm{8}\right)=\mathrm{7}…