Question Number 132715 by Dwaipayan Shikari last updated on 16/Feb/21 $$\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{3}} }−\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{4}^{\mathrm{3}} }−\frac{\mathrm{1}}{\mathrm{5}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{7}^{\mathrm{3}} }−\frac{\mathrm{1}}{\mathrm{8}^{\mathrm{3}} }+… \\ $$ Answered by Olaf last updated on…
Question Number 67148 by Cmr 237 last updated on 29/Aug/19 $$\mathrm{explicitez}\:\:\:\mathrm{la}\:\mathrm{suite}\:\mathrm{u}_{\mathrm{n}} \mathrm{definie}\:\mathrm{par}\:\mathrm{la}\:\mathrm{relation}; \\ $$$$\begin{cases}{\mathrm{u}_{\mathrm{0}} =\mathrm{0},\:\mathrm{u}_{\mathrm{1}} =\mathrm{1}}\\{\mathrm{u}_{\mathrm{n}+\mathrm{2}} =\mathrm{u}_{\mathrm{n}+\mathrm{1}} +\mathrm{u}_{\mathrm{n}} \:\:\:\forall\mathrm{n}\in\nmid\boldsymbol{\mathrm{N}}}\end{cases} \\ $$$$\boldsymbol{{u}}_{\boldsymbol{{n}}} =???????? \\ $$$$−\mathrm{calculer}\:\mathrm{la}\:\mathrm{lim}\underset{\mathrm{n}\rightarrow\infty} {\:}\frac{\mathrm{u}_{\mathrm{n}+\mathrm{1}}…
Question Number 1594 by 123456 last updated on 24/Aug/15 $${f}\left({x}\right)=\underset{\mathrm{0}} {\overset{{x}} {\int}}{t}^{{x}} {dt},{x}>−\mathrm{1} \\ $$$$\underset{{x}\rightarrow−\mathrm{1}^{+} } {\mathrm{lim}}{f}\left({x}\right)=? \\ $$$${f}\left({x}+\mathrm{1}\right)−{f}\left({x}\right)=? \\ $$ Commented by 112358 last…
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…