Question Number 1616 by 123456 last updated on 27/Aug/15 $$\mathrm{lets}\:\mathrm{two}\:\mathrm{sets}\:\mathrm{A},\mathrm{B}\:\mathrm{and}\:\mathrm{take}\:\mid\mathrm{X}\mid\:\mathrm{the}\:\mathrm{number} \\ $$$$\mathrm{of}\:\mathrm{elements}\:\mathrm{of}\:\mathrm{the}\:\mathrm{set}\:\mathrm{X},\:\mathrm{them} \\ $$$$\mathrm{proof}\:\mathrm{or}\:\mathrm{give}\:\mathrm{a}\:\mathrm{counter}\:\mathrm{example}\:\mathrm{that} \\ $$$$\mathrm{if}\:\mid\mathrm{A}\cup\mathrm{B}\mid=\infty\:\mathrm{and}\:\mid\mathrm{A}\cap\mathrm{B}\mid=\infty\:\mathrm{then}\:\mid\mathrm{A}\mid=\infty\:\mathrm{and}\:\mid\mathrm{B}\mid=\infty \\ $$ Commented by 112358 last updated on 27/Aug/15…
Question Number 67148 by Cmr 237 last updated on 29/Aug/19 $$\mathrm{explicitez}\:\:\:\mathrm{la}\:\mathrm{suite}\:\mathrm{u}_{\mathrm{n}} \mathrm{definie}\:\mathrm{par}\:\mathrm{la}\:\mathrm{relation}; \\ $$$$\begin{cases}{\mathrm{u}_{\mathrm{0}} =\mathrm{0},\:\mathrm{u}_{\mathrm{1}} =\mathrm{1}}\\{\mathrm{u}_{\mathrm{n}+\mathrm{2}} =\mathrm{u}_{\mathrm{n}+\mathrm{1}} +\mathrm{u}_{\mathrm{n}} \:\:\:\forall\mathrm{n}\in\nmid\boldsymbol{\mathrm{N}}}\end{cases} \\ $$$$\boldsymbol{{u}}_{\boldsymbol{{n}}} =???????? \\ $$$$−\mathrm{calculer}\:\mathrm{la}\:\mathrm{lim}\underset{\mathrm{n}\rightarrow\infty} {\:}\frac{\mathrm{u}_{\mathrm{n}+\mathrm{1}}…
Question Number 1613 by 112358 last updated on 26/Aug/15 $$\mathrm{Compute}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}−\mathrm{1}}{{logx}}{dx}\:. \\ $$ Commented by 123456 last updated on 27/Aug/15 $$\mathrm{I}=\mathrm{ln}\:\mathrm{10}\:\mathrm{ln}\:\mathrm{2} \\…
Question Number 1611 by Rasheed Soomro last updated on 26/Aug/15 $$\mathrm{A}\:\mathrm{right}\:\mathrm{angled}\:\mathrm{triangle}\:\mathrm{has}\:\mathrm{fixed}\:\mathrm{hypotenuse}\:\mathrm{measuring} \\ $$$$\mathrm{h}\:\mathrm{units}.\:\mathrm{What}\:\mathrm{are}\:\mathrm{the}\:\mathrm{measures}\:\:\mathrm{of}\:\mathrm{its}\:\mathrm{legs}, \\ $$$$\mathrm{for}\:\boldsymbol{\mathrm{maximum}}\:\boldsymbol{\mathrm{perimeter}}\:\mathrm{P}\:\mathrm{units}. \\ $$$$\mathrm{Will}\:\mathrm{the}\:\mathrm{area}\:\mathrm{be}\:\mathrm{also}\:\mathrm{maximum},\:\mathrm{when}\:\mathrm{the}\:\mathrm{perimeter}\:\mathrm{be} \\ $$$$\mathrm{maximum}? \\ $$ Commented by Rasheed Soomro…
Question Number 132683 by otchereabdullai@gmail.com last updated on 15/Feb/21 $$\mathrm{A}\:\mathrm{particle}\:\mathrm{in}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{line}\:\mathrm{with} \\ $$$$\mathrm{uniform}\:\mathrm{deceleration}\:\mathrm{has}\:\mathrm{a}\:\mathrm{velocity}\:\mathrm{of} \\ $$$$\mathrm{40ms}^{−\mathrm{1}} \:\mathrm{at}\:\mathrm{point}\:\mathrm{P}\:,\:\mathrm{20ms}^{−\mathrm{1}} \:\mathrm{at}\:\mathrm{point}\:\mathrm{Q} \\ $$$$\mathrm{and}\:\mathrm{comes}\:\mathrm{to}\:\mathrm{rest}\:\mathrm{at}\:\mathrm{point}\:\mathrm{R}\:\mathrm{where}\: \\ $$$$\mathrm{QR}=\:\mathrm{50m}.\:\mathrm{calculate}\:\mathrm{the} \\ $$$$\left(\mathrm{i}\right)\:\mathrm{Distance}\:\mathrm{PQ} \\ $$$$\left(\mathrm{ii}\right)\mathrm{Time}\:\mathrm{taken}\:\mathrm{to}\:\mathrm{cover}\:\mathrm{PQ} \\…
Question Number 132682 by otchereabdullai@gmail.com last updated on 15/Feb/21 $$\mathrm{expand}\:\mathrm{1}−\mathrm{x}^{\mathrm{8}} \\ $$ Answered by MJS_new last updated on 15/Feb/21 $$\mathrm{1}−{x}^{\mathrm{8}} =\left(\mathrm{1}−{x}^{\mathrm{4}} \right)\left(\mathrm{1}+{x}^{\mathrm{4}} \right)=\left(\mathrm{1}−{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{\mathrm{4}}…
Question Number 1608 by 112358 last updated on 26/Aug/15 $${Find}\:{the}\:{limit}\:{of}\:{this}\:{sequence}. \\ $$$$\sqrt{\mathrm{2}},\sqrt{\mathrm{2}\sqrt{\mathrm{2}}},\sqrt{\mathrm{2}\sqrt{\mathrm{2}\sqrt{\mathrm{2}}}},\sqrt{\mathrm{2}\sqrt{\mathrm{2}\sqrt{\mathrm{2}\sqrt{\mathrm{2}}}}},… \\ $$$${Show}\:{that}\:{the}\:{sum}\:{of}\:{the} \\ $$$${terms}\:{of}\:{this}\:{infinite}\:{sequence} \\ $$$${does}\:{not}\:{converge}. \\ $$ Commented by Rasheed Ahmad last…
Question Number 67138 by mhmd last updated on 23/Aug/19 $${find}\:{the}\:{area}\:{abounded}\:{y}=\sqrt{{x}} \\ $$$${and}\:{y}={x}−\mathrm{2}? \\ $$ Commented by mr W last updated on 23/Aug/19 $${sir}:\:{you}\:{don}'{t}\:{need}\:{to}\:{repeat}\:{the} \\ $$$${same}\:{question}\:{so}\:{frequently}.…
Question Number 1603 by 123456 last updated on 25/Aug/15 $$\frac{{f}\left({x}\right)}{{f}'\left({x}\right)}=\frac{{f}'\left({x}\right)}{{f}\left({x}\right)} \\ $$$${f}\left({x}\right)= \\ $$ Answered by Rasheed Soomro last updated on 28/Aug/15 $$\left[\:{f}\:'\left({x}\right)\:\right]^{\mathrm{2}} =\left[\:{f}\left({x}\right)\:\right]^{\mathrm{2}} \\…
Question Number 1602 by 112358 last updated on 25/Aug/15 $${Show}\:{that}\: \\ $$$$\frac{{d}}{{dy}}\int_{{g}_{\mathrm{1}} \left({y}\right)} ^{{g}_{\mathrm{2}} \left({y}\right)} {f}\left({x},{y}\right){dx}=\int_{{g}_{\mathrm{1}} \left({y}\right)} ^{{g}_{\mathrm{2}} \left({y}\right)} \frac{\partial{f}}{\partial{y}}\left({x},{y}\right){dx}+{g}_{\mathrm{2}} ^{'} \left({y}\right){f}\left({g}_{\mathrm{2}} \left({y}\right),{y}\right)−{g}_{\mathrm{1}} ^{'} \left({y}\right){f}\left({g}_{\mathrm{1}}…