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…
Question Number 67482 by Rasheed.Sindhi last updated on 27/Aug/19 $${I}\:{have}\:{tried}\:{to}\:{solve}\:{Q}#\mathrm{67299} \\ $$$${Please}\:{see}\:{and}\:{give}\:{critical}\:{remarks} \\ $$ Commented by mr W last updated on 28/Aug/19 $${your}\:{solution}\:{is}\:{correct}\:{sir}.\:{but}\:{i}'{m} \\ $$$${not}\:{sure}\:{if}\:{the}\:{solution}\:{is}\:{unique}.…
Question Number 1936 by 123456 last updated on 25/Oct/15 $${f}^{\mathrm{2}} \left({x}\right)−{f}\left({x}^{\mathrm{2}} \right)={a}\:\left[\mathrm{G}.\mathrm{Q1902}\right] \\ $$$${f}\left({x}\right)=? \\ $$ Commented by prakash jain last updated on 25/Oct/15 $$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{think}\:\mathrm{that}\:\mathrm{a}\:\mathrm{solution}\:\mathrm{exists}\:\mathrm{except}…
Question Number 67471 by AnjanDey last updated on 27/Aug/19 $$\boldsymbol{{Evaluate}}:\int\sqrt{{x}\sqrt{{x}+\mathrm{1}}}\:{dx} \\ $$ Commented by MJS last updated on 28/Aug/19 $$\int\sqrt{{x}\sqrt{{x}+\mathrm{1}}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{{x}}\:\rightarrow\:{dx}=\mathrm{2}\sqrt{{x}}{dt}\right] \\ $$$$=\mathrm{2}\int{t}^{\mathrm{2}} \left({t}^{\mathrm{2}}…
Question Number 1862 by 123456 last updated on 17/Oct/15 $${f}\left[{x}−{f}\left({y}\right)\right]={f}\left({x}\right)−{f}\left({y}\right),\forall\left({x},{y}\right)\in\mathbb{R} \\ $$$${f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${f}\left({x}\right)=? \\ $$ Answered by prakash jain last updated on 18/Oct/15 $${f}\left({x}\right)={x}\:\mathrm{is}\:\mathrm{one}\:\mathrm{solution}.…