Category: Relation and Functions

Question Number 68034 by mathmax by abdo last updated on 03/Sep/19 $$letf\left(x\right)=e^{-x},2\pi periodicdeveloppfatfourierserie.$$ Commented by mathmax by abdo last updated on 07/Sep/19 $${f}\left({x}\right)\:=\sum_{{n}=−\infty}…

Question Number 68019 by mathmax by abdo last updated on 03/Sep/19 $$letF\left(x\right)={\int }_x^{x^2+1}{e}^{-2t}sin\left(xt\right)dt$$$$determineF{}^{{}^{\prime }}\left(x\right)andcalculate{lim}_{x\to 0}F\left(x\right).$$$$$$ Commented…

Question Number 68001 by mathmax by abdo last updated on 03/Sep/19 $$letF\left(x\right)={\int }_{2x}^{x^2+1}\frac{e^{-xt}}{x+2t}dtcalculateF{}^{{}^{\prime }}\left(x\right)$$ Commented by mathmax by abdo last…

Question Number 67974 by mathmax by abdo last updated on 02/Sep/19 $$letF\left(x\right)={\int }_x^{x^2}\frac{arctan\left(xt\right)}{x^2+t^2}dtcalculateF{}^{{}^{\prime }}\left(x\right).$$ Commented by mathmax by abdo…

Question Number 133431 by Algoritm last updated on 22/Feb/21 Answered by benjo_mathlover last updated on 22/Feb/21 $${\mathrm{x}}^2\mathrm{y}-5\mathrm{xy}-\mathrm{y}={\mathrm{x}}^2-3\mathrm{x}-1$$$$(\mathrm{y}-1){\mathrm{x}}^2-(5\mathrm{y}-3)\mathrm{x}+1-\mathrm{y}=0$$$$\mathrm{x}\:=\:\frac{\mathrm{5y}−\mathrm{3}\pm\sqrt{\left(\mathrm{5y}−\mathrm{3}\right)^{\mathrm{2}} −\mathrm{4}\left(\mathrm{y}−\mathrm{1}\right)\left(\mathrm{1}−\mathrm{y}\right)}}{\mathrm{2}\left(\mathrm{y}−\mathrm{1}\right)}…