Question Number 1125 by 123456 last updated on 18/Jun/15 $${f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${g}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${f}\left({x}+{y}\right)={f}\left({x}\right)+{g}\left({y}\right) \\ $$$${g}\left({xy}\right)={f}\left({x}\right){g}\left({y}\right) \\ $$$${f}\left({x}\right)=? \\ $$$${g}\left({x}\right)=? \\ $$ Commented by 123456…
Question Number 132198 by benjo_mathlover last updated on 12/Feb/21 $$\mathrm{If}\:\begin{cases}{\mathrm{16}^{{a}+{b}} \:=\:\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}}\\{\mathrm{16}^{{b}+{c}} \:=\:\mathrm{2}}\\{\mathrm{16}^{{a}+{c}} \:=\:\mathrm{2}\sqrt{\mathrm{2}}}\end{cases} \\ $$$$\:\mathrm{then}\:\mathrm{c}\:=\:\_\_\: \\ $$ Answered by EDWIN88 last updated on 12/Feb/21 $$\mathrm{eq}\left(\mathrm{1}\right)\:\mathrm{16}^{\mathrm{2}\left(\mathrm{a}+\mathrm{b}\right)}…
Question Number 1124 by 123456 last updated on 17/Jun/15 $$\mathrm{lets}\:{f}:\left[\mathrm{0},\mathrm{1}\right]\rightarrow\mathbb{R}\:\mathrm{given}\:\mathrm{by} \\ $$$${f}\left({x}\right)=\begin{cases}{{x}}&{{x}\in\mathbb{Q}}\\{\mathrm{1}−{x}}&{{x}\notin\mathbb{Q}}\end{cases} \\ $$$$\mathrm{is}\:{f}\:\mathrm{continuos}\:\mathrm{at}\:{x}=\mathrm{1}/\mathrm{2}? \\ $$$$\mathrm{is}\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{fdx}\:\mathrm{riemann}\:\mathrm{integrable}? \\ $$$$\mathrm{is}\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{fdx}\:\mathrm{lebesgue}\:\mathrm{integable}? \\ $$ Commented…
Question Number 132192 by benjo_mathlover last updated on 12/Feb/21 $$\:\int\:\frac{\mathrm{dx}}{\mathrm{csc}\:\mathrm{x}\:+\:\mathrm{sec}\:\mathrm{x}} \\ $$ Answered by Dwaipayan Shikari last updated on 12/Feb/21 $$\int\frac{{sinx}\:{cosx}}{{sinx}+{cosx}}{dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int{sinx}+{cosx}−\frac{\mathrm{1}}{{sinx}+{cosx}}{dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\left({sinx}−{cosx}\right)−\int\frac{{dt}}{\mathrm{1}−{t}^{\mathrm{2}}…
Question Number 132195 by aurpeyz last updated on 12/Feb/21 $${Aspherical}\:{satelite}\:{orbiting}\:{Earth}\:{is} \\ $$$${lighted}\:{on}\:{one}\:{side}\:{by}\:{the}\:{sun}\:{with}\:{intensity} \\ $$$$\mathrm{340}{W}/{m}^{\mathrm{2}} .\:{If}\:{the}\:{radius}\:{of}\:{the}\: \\ $$$${satelite}\:{is}\:\mathrm{1}{m}.\:{what}\:{power}\:{is}\: \\ $$$${incident}\:{upon}\:{it}? \\ $$ Answered by ajfour last…
Question Number 66656 by Tanmay chaudhury last updated on 18/Aug/19 Commented by Rahul Kumar last updated on 18/Aug/19 $${please}\:{answer}\:{the}\:{question}. \\ $$ Answered by mr W…
Question Number 132194 by aurpeyz last updated on 12/Feb/21 Commented by mr W last updated on 12/Feb/21 $$\frac{{d}\theta}{{dr}}=\mathrm{3}{r}^{\mathrm{2}} −\mathrm{1} \\ $$$$\Delta\theta\approx\left(\mathrm{3}{r}^{\mathrm{2}} −\mathrm{1}\right)\Delta{r}=\left(\mathrm{3}×\mathrm{1}^{\mathrm{2}} −\mathrm{1}\right)×\mathrm{0}.\mathrm{05}=\mathrm{0}.\mathrm{1} \\ $$…
Question Number 1120 by 123456 last updated on 17/Jun/15 $$\mathrm{given}\:{f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${f}\left({x}\right)={a}_{{n}} {x}^{{n}} +\centerdot\centerdot\centerdot+{a}_{\mathrm{0}} \: \\ $$$$\mathrm{with}\:{a}_{{n}} \neq\mathrm{0},\:{a}_{{i}} \in\mathbb{R},{i}\in\left\{\mathrm{0},\mathrm{1},…,{n}\right\},{n}\in\mathbb{N}^{\ast} \\ $$$$\mathrm{supose}\:\mathrm{that}\:{x}_{\mathrm{1}} ,…,{x}_{{n}} \\ $$$$\mathrm{are}\:\mathrm{roots}\:\mathrm{the}\:{n}\:\mathrm{roots}\:\mathrm{of}\:{f}\left({x}\right) \\…
Question Number 132191 by rs4089 last updated on 12/Feb/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{log}_{{e}} \left({x}+\mathrm{1}\right)}{{x}\left({x}^{\mathrm{2}} +\mathrm{1}\right)}{dx} \\ $$ Answered by mathmax by abdo last updated on 12/Feb/21…
Question Number 1117 by 123456 last updated on 17/Jun/15 $${a}_{\mathrm{0}} =\mathrm{1} \\ $$$${a}_{{n}} =\frac{\sqrt{{a}_{{n}−\mathrm{1}} }}{{a}_{{n}−\mathrm{1}} }+\mathrm{1} \\ $$$$\underset{{n}\rightarrow+\infty} {\mathrm{lim}}\:{a}_{{n}} =? \\ $$ Commented by 123456…