Category: Relation and Functions

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)}…

Question Number 67795 by mathmax by abdo last updated on 31/Aug/19 $$let{A}_p={\int }_0^{\pi }{x}^{p}cos\left(nx\right)dx$$$$1)calculate{A}_0,A_1,A_2$$$$2)determinearelationofrecurrencebetween{A}_p$$ Commented…

Question Number 2205 by prakash jain last updated on 08/Nov/15 $$f\left(x\right)+f\left(\frac{x-1}{x}\right)=1+x$$$$f\left(x\right)=?$$ Commented by Yozzi last updated on 08/Nov/15 $$f\left(x\right)+f(1-\frac{1}{x})=1+x$$$$\Rightarrow{f}^{'}…