Question Number 1573 by 123456 last updated on 20/Aug/15 $$\underset{\epsilon\rightarrow+\infty} {\mathrm{lim}}\:\underset{\mathrm{0}} {\overset{\epsilon} {\int}}\epsilon^{−{t}} {dt}=? \\ $$ Commented by 112358 last updated on 21/Aug/15 $${Let}\:{I}\left(\epsilon\right)=\int_{\mathrm{0}} ^{\:\epsilon}…
Question Number 1559 by 123456 last updated on 19/Aug/15 $$\mathrm{find}\:\mathrm{complex}\:\mathrm{number}\:\alpha,\beta\:\mathrm{such}\:\mathrm{that} \\ $$$$\alpha^{{n}} =\beta^{{m}} \\ $$$$\beta^{{u}} =\alpha^{{v}} \\ $$$${n},{m},{u},{v}\in\mathbb{Z} \\ $$$$\boldsymbol{{Q}}\mathrm{1498} \\ $$ Answered by Rasheed…
Question Number 1557 by 123456 last updated on 19/Aug/15 $$\mathrm{find}\:\alpha,\beta,\gamma\:\mathrm{such}\:\mathrm{that} \\ $$$$\alpha=\beta^{\mathrm{2}} \\ $$$$\beta^{\mathrm{3}} =\gamma^{\mathrm{4}} \\ $$$$\gamma^{\mathrm{5}} =\alpha^{\mathrm{6}} \\ $$ Commented by 123456 last updated…
Question Number 1472 by 123456 last updated on 11/Aug/15 $$\mathrm{find}\:{f}:\left[\mathrm{0},\mathrm{1}\right]\rightarrow\mathbb{R}\:\mathrm{such}\:\mathrm{that} \\ $$$${a}.\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{fdt}=\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\sqrt{\mathrm{1}+\left(\frac{{df}}{{dt}}\right)^{\mathrm{2}} }{dt} \\ $$$${b}.\forall{x}\in\left[\mathrm{0},\mathrm{1}\right] \\ $$$$\underset{\mathrm{0}} {\overset{{x}} {\int}}{fdt}=\underset{\mathrm{0}} {\overset{{x}} {\int}}\sqrt{\mathrm{1}+\left(\frac{{df}}{{dt}}\right)^{\mathrm{2}}…
Question Number 67004 by sandeepkeshari0797@gmail.com last updated on 21/Aug/19 Answered by $@ty@m123 last updated on 21/Aug/19 $${Its}\:{repeatation}\:{of}\:{Q}.\:{No}.\:\mathrm{66356}. \\ $$$${Already}\:{answered}. \\ $$ Commented by sandeepkeshari0797@gmail.com last…
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 $${can}\:{any}\:{one}\:{help}\:{me}…{please}…
Question Number 1462 by 123456 last updated on 07/Aug/15 $$\mathrm{can}\:\mathrm{a}\:\mathrm{function}\:{f}_{{n}} :\mathbb{R}\rightarrow\mathbb{R}\:\mathrm{be}\:\mathrm{such}\:\mathrm{that} \\ $$$$\underset{{n}=\mathrm{0}} {\overset{+\infty} {\sum}}{f}_{{n}} \left({x}\right)\:\mathrm{converge}\:\mathrm{for}\:{x}\in\mathbb{Q}\:\mathrm{and}\:\mathrm{diverge} \\ $$$$\mathrm{for}\:{x}\in\mathbb{R}\backslash\mathbb{Q}? \\ $$ Commented by prakash jain last…
Question Number 1456 by 123456 last updated on 06/Aug/15 $$ \mathrm{S}^{\mathrm{1}} =\left\{\left({x},{y}\right)\in\mathbb{R}^{\mathrm{2}} :{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{1}\right\} \\ $$$$\varphi:\left[\mathrm{0},\mathrm{4}\pi\right)\rightarrow\mathrm{E}^{\mathrm{1},\mathrm{1}} ,\mathrm{E}^{\mathrm{1},\mathrm{1}} \subset\mathbb{R}^{\mathrm{2}} \\ $$$$\varphi\left({t}\right)=\left(\mathrm{1}+\mathrm{cos}\:{t}\:\mathrm{sin}\:{t}\right)\left(\mathrm{cos}\:{t},\mathrm{sin}\:{t}\right) \\ $$$$\mathrm{S}^{\mathrm{1}} \cap\mathrm{E}^{\mathrm{1},\mathrm{1}} \neq\emptyset…
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Question Number 1454 by 123456 last updated on 06/Aug/15 $$\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…