Question Number 4950 by madscientist last updated on 25/Mar/16 $${what}\:{is}\:{a}\:{whole}\:{divided}\:{by}\:{diffrent}\:{amouts} \\ $$$${infinitly}\:{what}\:{does}\:{it}\:{sooner}\:{or}\:{later}\:{equal}? \\ $$ Commented by prakash jain last updated on 25/Mar/16 $$\mathrm{Successive}\:\mathrm{division}\:\mathrm{by}\:\mathrm{0}<{x}<\mathrm{1} \\ $$$$\underset{{n}\rightarrow\infty}…
Question Number 136023 by mathmax by abdo last updated on 18/Mar/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\mathrm{e}^{−\mathrm{z}^{\mathrm{2}} } \mathrm{dz}\:\:\mathrm{with}\:\mathrm{z}\:\mathrm{complex} \\ $$ Commented by yutytfjh67ihd last updated on 25/Mar/21…
Question Number 136022 by mathmax by abdo last updated on 18/Mar/21 $$\left.\mathrm{1}\right)\mathrm{decompose}\:\mathrm{inside}\:\mathrm{C}\left(\mathrm{x}\right)\:\mathrm{the}\:\mathrm{fraction}\:\mathrm{F}\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{n}} } \\ $$$$\left.\mathrm{2}\right)\:\mathrm{find}\:\int_{\mathrm{1}} ^{\infty} \:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{n}} } \\ $$ Terms of Service…
Question Number 70482 by Mikaell last updated on 04/Oct/19 $$\int\frac{{sin}^{\mathrm{3}} {x}}{\:\sqrt{{cosx}}}{dx} \\ $$ Commented by kaivan.ahmadi last updated on 04/Oct/19 $${u}={cosx}\Rightarrow{du}=−{sinxdx} \\ $$$${sin}^{\mathrm{3}} {x}={sinxsin}^{\mathrm{2}} {x}={sinx}\left(\mathrm{1}−{cos}^{\mathrm{2}}…
Question Number 70483 by Mikaell last updated on 04/Oct/19 $$\int\frac{{ln}\mathrm{2}{x}}{{ln}\mathrm{4}{x}}.\frac{{dx}}{{x}} \\ $$ Commented by peter frank last updated on 04/Oct/19 $${thankx} \\ $$ Commented by…
Question Number 4946 by FilupSmith last updated on 25/Mar/16 $$\mathrm{Lets}\:\mathrm{say}\:{y}={f}\left({x}\right):\forall{x}\in\mathbb{R},{y}\in\mathbb{R} \\ $$$$ \\ $$$$\mathrm{if}\:{a}=\mathrm{constent} \\ $$$$\mathrm{Does}\:\mathrm{there}\:\mathrm{exist}\:{f}\left({a}\right)={a} \\ $$$$\mathrm{for}\:\mathrm{any}\:\mathrm{function}\:{y}={f}\left({x}\right)? \\ $$$$\mathrm{Please}\:\mathrm{prove}/\mathrm{disprove} \\ $$ Commented by prakash…
Question Number 4943 by madscientist last updated on 25/Mar/16 $$\mathrm{1}\:{whole}\:\boldsymbol{\div}\frac{\mathrm{1}}{\mathrm{4}}=\mathrm{0}.\mathrm{25}\boldsymbol{\div}\frac{\mathrm{1}}{\mathrm{4}}=\mathrm{0}.\mathrm{0625}\boldsymbol{\div}\frac{\mathrm{1}}{\mathrm{4}}…\infty \\ $$$$\mathrm{1}\:{whole}\:{divided}\:{by}\:\frac{\mathrm{1}}{\mathrm{4}}\:{infinitly}\:=\:{what} \\ $$$${how}?\:{what}\:{would}\:{the}\:{formula}\:{look}\:{like}? \\ $$ Commented by FilupSmith last updated on 25/Mar/16 $$\mathrm{1}\boldsymbol{\div}\frac{\mathrm{1}}{\mathrm{4}}\neq\mathrm{0}.\mathrm{25} \\…
Question Number 4942 by prakash jain last updated on 24/Mar/16 $$\mathrm{If}\:{p}\:\mathrm{is}\:\mathrm{a}\:\mathrm{prime}\:\mathrm{number}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{5},\:\mathrm{the}\:\mathrm{prove} \\ $$$$\mathrm{that}\:{p}\:\mathrm{mod}\:\mathrm{6}\:\equiv\mathrm{1}\:\mathrm{or}\:{p}\:\mathrm{mod}\:\mathrm{6}\equiv\mathrm{5}. \\ $$$$\mathrm{i}.\mathrm{e}.\:\mathrm{All}\:\mathrm{prime}\:\mathrm{numbers}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{5}\:\mathrm{leave}\:\mathrm{a} \\ $$$$\mathrm{remainder}\:\mathrm{of}\:\mathrm{1}\:\mathrm{or}\:\mathrm{5}\:\mathrm{when}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{6}. \\ $$ Commented by Yozzii last updated on…
Question Number 4941 by madscientist last updated on 25/Mar/16 $${if}\:{i}\:{had}\:{a}\:{grid}\:{with}\:\mathrm{4}\:{quadrants}\:{and}\:{i}\:{shaded}\:{a}\:\: \\ $$$${quarter}\:{of}\:{it}\:{and}\:{chose}\:{one}\:{of}\:{the}\:\mathrm{4}\:{quadrants}\:{to}\:{form}\:{a}\:{new}\:{grid} \\ $$$${and}\:{shaded}\:{it}\:{and}\:{repeated}\:{the}\:{process}\:{infinitly}\:{what}\: \\ $$$${is}\:{the}\:{amount}\:{of}\:{the}\:{shaded}\:{area}? \\ $$$${and}\:{what}\:{formula}\:{will}\:{solve}\:{it}? \\ $$ Answered by FilupSmith last updated…
Question Number 4939 by Yozzii last updated on 24/Mar/16 $$\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\left(−\mathrm{1}\right)^{{k}+\mathrm{1}} {k}^{\mathrm{2}} }{{k}^{\mathrm{3}} +\mathrm{1}}\right)=? \\ $$ Commented by prakash jain last updated on 24/Mar/16…