Question Number 67659 by Rio Michael last updated on 29/Aug/19 $${Help}\:{me}\:{obtain}\:\:\:{the}\:{value}\:{of}\:\:{e}\:{from} \\ $$$$\:\left(\mathrm{1}\:+\:\frac{\mathrm{1}}{{n}}\right)^{{n}} \:\:{how}\:{do}\:{i}\:{go}\:{about}\:{it}. \\ $$ Commented by Abdo msup. last updated on 30/Aug/19 $${A}_{{n}}…
Question Number 2111 by 123456 last updated on 03/Nov/15 $$\mathrm{lets}\:{f}:\mathbb{R}^{\mathrm{2}} \rightarrow\mathbb{R} \\ $$$$\mathrm{does} \\ $$$$\frac{\partial{f}}{\partial{x}}=\frac{\partial}{\partial{x}}\underset{\mathrm{0}} {\overset{{x}} {\int}}\frac{\partial{f}}{\partial{y}}{dy}\:\:\:? \\ $$ Answered by prakash jain last updated…
Question Number 67631 by Hassen_Timol last updated on 29/Aug/19 $$ \\ $$$$ \\ $$$$\:\:\:\mathrm{Can}\:\mathrm{you}\:\mathrm{please}\:\mathrm{tell}\:\mathrm{me},\:\mathrm{where}\:\mathrm{does}\:\mathrm{this}\: \\ $$$$\:\:\:\mathrm{formula}\:\mathrm{come}\:\mathrm{from}? \\ $$$$\:\:\:\mathrm{And}\:\mathrm{what}\:\mathrm{means}\:\mathrm{the}\:\mathrm{factorial}\:\mathrm{of}\:\mathrm{a}\:\mathrm{non}- \\ $$$$\:\:\:\mathrm{integer}\:\mathrm{number}? \\ $$$$ \\ $$$$\:\:\:\:\:\:\pi\:=\:\left(\frac{\mathrm{1}}{\mathrm{2}}!\right)^{\mathrm{2}} ×\:\mathrm{4}…
Question Number 2075 by 123456 last updated on 01/Nov/15 $${f}^{−\mathrm{1}} \left({x}\right)={f}'\left({x}\right) \\ $$$${f}\left({x}\right)=?? \\ $$ Commented by Yozzi last updated on 01/Nov/15 $$\mathrm{1}={f}\left({x}\right){f}^{'} \left({x}\right) \\…
Question Number 133103 by 777316 last updated on 18/Feb/21 Commented by bemath last updated on 18/Feb/21 $$\mathrm{If}\:\mathrm{x}+\mathrm{y}\:=\:\mathrm{c}\:\mathrm{then}\:\mathrm{ln}\:\mathrm{x}+\mathrm{ln}\:\mathrm{y}\:\neq\:\mathrm{ln}\:\mathrm{c}\: \\ $$$$\mathrm{sir}\: \\ $$ Commented by malwan last…
Question Number 133069 by Dwaipayan Shikari last updated on 18/Feb/21 Commented by Dwaipayan Shikari last updated on 18/Feb/21 $${One}\:{can}\:{stretch}\:{and}\:{reform}\:{sides}\:{AB}\:\:{and}\:{AC}\:,\:{by}\: \\ $$$${considering}\:{length}\:\:{BC}\:{as}\:{constant}.\:{the}\:{angle}\: \\ $$$$\phi\:{can}\:{change}.\:{Find}\:{the}\:{relationship}\:{of}\:{changes}\:{between}\:{Side}\: \\ $$$${AB}\:,\:{AC}\:{and}\:{angle}\:\phi…
given-x-y-continuous-and-differenriable-such-that-x-x-t-y-y-t-does-d-2-y-dx-2-d-2-y-dt-2-d-2-x-dt-2-
Question Number 1996 by 123456 last updated on 28/Oct/15 $$\mathrm{given}\:{x},{y}\:\mathrm{continuous}\:\mathrm{and}\:\mathrm{differenriable} \\ $$$$\mathrm{such}\:\mathrm{that} \\ $$$$\begin{cases}{{x}={x}\left({t}\right)}\\{{y}={y}\left({t}\right)}\end{cases} \\ $$$$\mathrm{does} \\ $$$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }=\frac{\frac{{d}^{\mathrm{2}} {y}}{{dt}^{\mathrm{2}} }}{\frac{{d}^{\mathrm{2}} {x}}{{dt}^{\mathrm{2}} }}? \\…
Question Number 1985 by 123456 last updated on 27/Oct/15 $${f}:\left[{a},{b}\right]\rightarrow\mathbb{R} \\ $$$$\underset{{a}} {\overset{{b}} {\int}}{fdx}=\underset{{a}} {\overset{{b}} {\int}}\sqrt{\mathrm{1}+\left(\frac{{df}}{{dx}}\right)^{\mathrm{2}} }{dx} \\ $$$$\mathrm{does} \\ $$$$\pi\underset{{a}} {\overset{{b}} {\int}}{f}^{\mathrm{2}} {dx}=\mathrm{2}\pi\underset{{a}} {\overset{{b}}…
Question Number 1970 by 123456 last updated on 27/Oct/15 $${f}:\left[\mathrm{0},+\infty\right)\rightarrow\mathbb{R} \\ $$$${xf}\left({x}\right)={f}\left[{f}\left({x}\right)\right]{f}\left({x}\right) \\ $$$${f}\left({x}\right)=? \\ $$ Answered by prakash jain last updated on 27/Oct/15 $${f}\left({x}\right)\neq\mathrm{0}\:\mathrm{then}\:{f}\left({f}\left({x}\right)={x}\right.…
Question Number 1964 by 123456 last updated on 26/Oct/15 $$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }=\frac{{cy}}{{x}^{\mathrm{2}} } \\ $$$${y}\left({x}\right)=? \\ $$ Answered by prakash jain last updated on 26/Oct/15…