Category: Relation and Functions

Question Number 144699 by mathmax by abdo last updated on 28/Jun/21 $$\mathrm{let}\mathrm{f}\left(\mathrm{x}\right)=\log \left(\mathrm{cht}\right)$$$$\mathrm{developp}\mathrm{f}\mathrm{at}\mathrm{fourier}\mathrm{serie}$$ Answered by Olaf_Thorendsen last updated on 28/Jun/21 $${f}\:\mathrm{is}\:\mathrm{not}\:\mathrm{periodic}\:! \…

Question Number 13601 by Tinkutara last updated on 21/May/17 $$\mathrm{Let}f:\mathbb{R}-\left\{\frac{3}{5}\right\}\to \mathbb{R}\mathrm{be}\mathrm{defined}\mathrm{by}$$$$f\left(x\right)=\frac{3x+2}{5x-3}.\mathrm{Then},$$$$\left(\mathrm{a}\right)f^{-1}\left(x\right)=x$$$$\left(\mathrm{b}\right)f^{-1}\left(x\right)=-f\left(x\right)$$$$\left(\mathrm{c}\right)fof\left(x\right)=-x$$$$\left(\mathrm{d}\right)f^{-1}\left(x\right)=\frac{1}{19}f\left(x\right)$$…

Question Number 79107 by mathmax by abdo last updated on 22/Jan/20 $$calculatef\left(a\right)={\int }_0^{\mathrm{\infty }}{e}^{-(x^2+\frac{a}{x^2})}dxwitha>0$$ Commented by mathmax by abdo last…

Question Number 79108 by mathmax by abdo last updated on 22/Jan/20 $$decomposeF\left(x\right)=\frac{{nx}^n}{x^{2n}+1}insideC\left(x\right)andR\left(x\right)(n⩾2)$$$$anddetermine{\int }_0^{+\mathrm{\infty }}F\left(x\right)dx$$ Commented by mathmax by abdo…

Question Number 79102 by mathmax by abdo last updated on 22/Jan/20 $$calculate{lim}_{x\to 0}\frac{ln(1+e^{-x^2})-ln\left(2\right)}{x^2}$$ Commented by mathmax by abdo last updated…