Category: Relation and Functions

Question Number 96656 by mathmax by abdo last updated on 03/Jun/20 $$\mathrm{let}\mathrm{g}\left(\mathrm{x}\right)=\frac{2}{\mathrm{cosx}}\mathrm{developp}\mathrm{f}\mathrm{at}\mathrm{fourier}\mathrm{serie}$$ Answered by mathmax by abdo last updated on 04/Jun/20 $$\mathrm{we}\:\mathrm{have}\:\mathrm{g}\left(\mathrm{x}\right)\:=\frac{\mathrm{2}}{\mathrm{cosx}}\:\Rightarrow\mathrm{g}\left(\mathrm{x}\right)\:=\frac{\mathrm{4}}{\mathrm{e}^{\mathrm{ix}} \:+\mathrm{e}^{−\mathrm{ix}}…

Question Number 96607 by bemath last updated on 03/Jun/20 $$\mathrm{It}\mathrm{is}\mathrm{given}\mathrm{that}\mathrm{f}\left(\mathrm{x}\right)\mathrm{is}\mathrm{a}\mathrm{function}$$$$\mathrm{defined}\mathrm{on}\mathbb{R},\mathrm{satisfying}\mathrm{f}\left(1\right)=1$$$$\mathrm{and}\mathrm{for}\mathrm{any}\mathrm{x}\in \mathbb{R},\mathrm{f}(\mathrm{x}+5)⩾\mathrm{f}\left(\mathrm{x}\right)+5$$$$\mathrm{and}\mathrm{f}(\mathrm{x}+1)⩽\mathrm{f}\left(\mathrm{x}\right)+1.\mathrm{If}\mathrm{g}\left(\mathrm{x}\right)=$$$$\mathrm{f}\left(\mathrm{x}\right)+1-\mathrm{x},\mathrm{then}\mathrm{g}\left(2002\right)=\mathrm{\_}\mathrm{\_}\mathrm{\_}$$ Commented by bobhans last updated…

Question Number 96570 by mathmax by abdo last updated on 02/Jun/20 $$\mathrm{solve}{\mathrm{xy}}^{{}^{″}}-({\mathrm{x}}^3+1){\mathrm{y}}^{{}^{\prime }}+2\mathrm{y}={\mathrm{x}}^2{\mathrm{e}}^{-\mathrm{x}}\mathrm{with}\mathrm{y}\left(\mathrm{o}\right)=1\mathrm{and}{\mathrm{y}}^{{}^{\prime }}\left(0\right)=-2$$ Terms of Service Privacy Policy…

Question Number 30871 by ajfour last updated on 27/Feb/18 $$If2f\left(x\right)+f(-x)=\frac{1}{x}\sin (x-\frac{1}{x})$$$$Find{\int }_{1/e}^{e}f\left(x\right)dx.$$ Commented by abdo imad last updated on 27/Feb/18 $${let}\:{complete}\:{the}\:{work}\:{of}\:{sir}\:{mrw}_{\mathrm{2}}…

Question Number 96377 by mathmax by abdo last updated on 01/Jun/20 $$\mathrm{if}\tan (\mathrm{x}+\mathrm{iy})=\mathrm{a}+\mathrm{ib}\mathrm{determine}\mathrm{x}\mathrm{and}\mathrm{y}\mathrm{interms}\mathrm{of}\mathrm{a}\mathrm{and}\mathrm{b}$$ Answered by mathmax by abdo last updated on 02/Jun/20 $$\mathrm{tan}\left(\mathrm{x}+\mathrm{iy}\right)\:=\mathrm{a}+\mathrm{ib}\:\Rightarrow\mathrm{x}+\mathrm{iy}\:=\mathrm{arctan}\left(\mathrm{a}+\mathrm{ib}\right)\:\mathrm{we}\:\mathrm{know} \…