Category: Relation and Functions

Question Number 17872 by Tinkutara last updated on 11/Jul/17 $$\mathrm{Solve}:$$$$\mid x-1\mid +\mid x\mid +\mid x+1\mid =x+2$$ Answered by ajfour last updated on 11/Jul/17 $$\mathrm{x}\in [0,1]$$ Answered…

Question Number 83403 by jagoll last updated on 02/Mar/20 $$\mathrm{what}\mathrm{is}\mathrm{range}\mathrm{function}$$$$\mathrm{y}=\frac{1}{{(\mathrm{x}-1)}^2}$$ Answered by MJS last updated on 02/Mar/20 $${y}=\frac{\mathrm{1}}{\left({x}−\mathrm{1}\right)^{\mathrm{2}} }\:\mathrm{defined}\:\mathrm{for}\:{x}\neq\mathrm{1} \…

Question Number 148812 by mathmax by abdo last updated on 31/Jul/21 $$\mathrm{find}\int \frac{\mathrm{dx}}{(\sqrt{\mathrm{x}}+\sqrt{\mathrm{x}+1})(\sqrt{\mathrm{x}-1}+\sqrt{\mathrm{x}})}$$ Answered by MJS_new last updated on 31/Jul/21 $$\int \frac{dx}{(\sqrt{x}+\sqrt{x+1})(\sqrt{x}+\sqrt{x-1})}=$$$$=\int\left(\frac{\mathrm{1}}{\left(\sqrt{{x}}+\sqrt{{x}+\mathrm{1}}\right)\left(\sqrt{{x}}+\sqrt{{x}−\mathrm{1}}\right)}×\frac{\left(\sqrt{{x}}−\sqrt{{x}+\mathrm{1}}\right)\left(\sqrt{{x}}−\sqrt{{x}−\mathrm{1}}\right)}{\left(\sqrt{{x}}−\sqrt{{x}+\mathrm{1}}\right)\left(\sqrt{{x}}−\sqrt{{x}−\mathrm{1}}\right)}\right){dx}= \…

Question Number 83254 by mathmax by abdo last updated on 29/Feb/20 $$letf\left(x\right)=arctan(2x-\frac{1}{x})$$$$find{f}^{\left(n\right)}\left(x\right){andf}^{\left(n\right)}\left(1\right)$$ Commented by mathmax by abdo last updated…

Question Number 83214 by mathmax by abdo last updated on 28/Feb/20 $$calculate{U}_n=\sum _{k=0}^n\frac{1}{3k+1}intermsof{H}_n=\sum _{k=1}^n\frac{1}{k}$$ Answered by ~blr237~ last updated…