Category: Others

Question Number 1472 by 123456 last updated on 11/Aug/15 $$\mathrm{find}\:{f}:\left[\mathrm{0},\mathrm{1}\right]\rightarrow\mathbb{R}\:\mathrm{such}\:\mathrm{that} \\ $$$${a}.\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{fdt}=\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\sqrt{\mathrm{1}+\left(\frac{{df}}{{dt}}\right)^{\mathrm{2}} }{dt} \\ $$$${b}.\forall{x}\in\left[\mathrm{0},\mathrm{1}\right] \\ $$$$\underset{\mathrm{0}} {\overset{{x}} {\int}}{fdt}=\underset{\mathrm{0}} {\overset{{x}} {\int}}\sqrt{\mathrm{1}+\left(\frac{{df}}{{dt}}\right)^{\mathrm{2}}…

Question Number 132537 by SLVR last updated on 15/Feb/21 $${If}\:{f}\left({x}\right)=\mathrm{8}{x}^{\mathrm{3}\:} +\mathrm{3}{x}\:{then}\:{lim}_{{x}\rightarrow\infty} \frac{{x}^{\mathrm{1}/\mathrm{3}} }{{f}^{−\mathrm{1}} \left(\mathrm{8}{x}\right)−{f}^{−\mathrm{1}} \left({x}\right)}\:{is} \\ $$ Commented by SLVR last updated on 15/Feb/21 $${can}\:{any}\:{one}\:{help}\:{me}…{please}…

Question Number 1456 by 123456 last updated on 06/Aug/15 $$ \mathrm{S}^{\mathrm{1}} =\left\{\left({x},{y}\right)\in\mathbb{R}^{\mathrm{2}} :{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{1}\right\} \\ $$$$\varphi:\left[\mathrm{0},\mathrm{4}\pi\right)\rightarrow\mathrm{E}^{\mathrm{1},\mathrm{1}} ,\mathrm{E}^{\mathrm{1},\mathrm{1}} \subset\mathbb{R}^{\mathrm{2}} \\ $$$$\varphi\left({t}\right)=\left(\mathrm{1}+\mathrm{cos}\:{t}\:\mathrm{sin}\:{t}\right)\left(\mathrm{cos}\:{t},\mathrm{sin}\:{t}\right) \\ $$$$\mathrm{S}^{\mathrm{1}} \cap\mathrm{E}^{\mathrm{1},\mathrm{1}} \neq\emptyset…

Question Number 1454 by 123456 last updated on 06/Aug/15 $$\mathrm{lets}\:{f}:\mathbb{R}\rightarrow\mathbb{R},\:\mathrm{if}\:\left({f}\bullet{f}\right)\left({x}\right)\:\mathrm{is}\:\mathrm{continuous} \\ $$$$\mathrm{proof}\:\mathrm{or}\:\mathrm{give}\:\mathrm{a}\:\mathrm{counter}\:\mathrm{example}\:\mathrm{that}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{continous}. \\ $$ Commented by 123456 last updated on 07/Aug/15 $${f}\left({x}\right)=\begin{cases}{\mathrm{3},{x}>\mathrm{0}}\\{\mathrm{2},{x}=\mathrm{0}}\\{\mathrm{1},{x}<\mathrm{0}}\end{cases} \\ $$ Commented…

Question Number 66985 by Mr Jor last updated on 21/Aug/19 $$\mathrm{The}\:\mathrm{external}\:\mathrm{length},\mathrm{width}\:\mathrm{and}\:\mathrm{height} \\ $$$$\mathrm{of}\:\mathrm{an}\:\mathrm{open}\:\mathrm{rectangular}\:\mathrm{container}\:\mathrm{are} \\ $$$$\mathrm{41cm},\mathrm{21cm}\:\mathrm{and}\:\mathrm{15}.\mathrm{5cm}\:\mathrm{respectively}. \\ $$$$\mathrm{The}\:\mathrm{thickness}\:\mathrm{of}\:\mathrm{the}\:\mathrm{material}\:\mathrm{making} \\ $$$$\mathrm{the}\:\mathrm{container}\:\mathrm{is}\:\mathrm{5mm}.\mathrm{If}\:\mathrm{the}\:\mathrm{container} \\ $$$$\mathrm{has}\:\mathrm{8litres}\:\mathrm{of}\:\mathrm{water},\mathrm{calculate}\:\mathrm{the} \\ $$$$\mathrm{internal}\:\mathrm{height}\:\mathrm{above}\:\mathrm{the}\:\mathrm{water}\:\mathrm{level}. \\ $$$$\:\:\:\:\:\:\:\:…