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Category: Relation and Functions

developp-at-fourier-serie-f-x-1-cosx-2sinx-

Question Number 143262 by Mathspace last updated on 12/Jun/21 $${developp}\:{at}\:{fourier}\:{serie} \\ $$$${f}\left({x}\right)=\frac{\mathrm{1}}{{cosx}\:+\mathrm{2}{sinx}} \\ $$ Answered by mathmax by abdo last updated on 13/Jun/21 $$\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\mathrm{cosx}+\mathrm{2sinx}}\:\Rightarrow\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\frac{\mathrm{e}^{\mathrm{ix}} +\mathrm{e}^{−\mathrm{ix}}…

find-lim-x-0-sin-1-cosx-1-cos-sinx-x-2-

Question Number 143255 by Mathspace last updated on 12/Jun/21 $${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \frac{{sin}\left(\mathrm{1}−{cosx}\right)+\mathrm{1}−{cos}\left({sinx}\right)}{{x}^{\mathrm{2}} } \\ $$ Answered by bramlexs22 last updated on 12/Jun/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\frac{\mathrm{sin}\:\left(\mathrm{1}−\mathrm{cos}\:{x}\right)}{\mathrm{1}−\mathrm{cos}\:{x}}.\left(\mathrm{1}−\mathrm{cos}\:{x}\right)+\mathrm{1}−\mathrm{cos}\:\left(\mathrm{sin}\:{x}\right)}{{x}^{\mathrm{2}} } \\…

find-the-value-of-n-1-1-n-n-2-n-1-n-2-n-3-

Question Number 143254 by Mathspace last updated on 12/Jun/21 $${find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)\left({n}+\mathrm{3}\right)} \\ $$ Answered by Olaf_Thorendsen last updated on 12/Jun/21 $${R}\left({n}\right)\:=\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)\left({n}+\mathrm{3}\right)}…