Question Number 132697 by liberty last updated on 15/Feb/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{condition}\:\mathrm{that}\:\mathrm{one} \\ $$$$\mathrm{root}\:\mathrm{of}\:{ax}^{\mathrm{2}} +{bx}+{c}\:=\:\mathrm{0}\:,{a}\neq\:\mathrm{0} \\ $$$$\mathrm{is}\:\mathrm{square}\:\mathrm{of}\:\mathrm{the}\:\mathrm{other}\:. \\ $$ Commented by liberty last updated on 16/Feb/21 $$\mathrm{okay}…
Question Number 1625 by 112358 last updated on 27/Aug/15 $${y}\left({x}\right)=\frac{\mathrm{1}}{{x}−{a}}\int_{{a}} ^{{x}} \sqrt{{t}+\sqrt{{t}+\sqrt{{t}+\sqrt{{t}+\sqrt{{t}+…}}}}}{dt} \\ $$$${x}\neq{a},\:{a}>\mathrm{0},{y}\left({x}\right)>\mathrm{0}. \\ $$$${Find}\:\:{y}\left(\mathrm{2}{a}\right). \\ $$ Answered by Rasheed Soomro last updated on…
Question Number 1624 by 112358 last updated on 27/Aug/15 $${Find}\:{the}\:{first}\:{derivative}\:{of} \\ $$$${y}\left({x}\right)=\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+…}}}}} \\ $$$${from}\:{first}\:{principles}.\: \\ $$$$ \\ $$ Commented by Rasheed Soomro last updated on…
Question Number 132693 by liberty last updated on 15/Feb/21 $$\mathrm{I}=\int\:\frac{{dx}}{{x}\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{3}} }\: \\ $$ Answered by EDWIN88 last updated on 15/Feb/21 $$\mathrm{Ostrogradsky}\:\mathrm{again} \\ $$$$\int\:\frac{{dx}}{{x}\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{3}}…
Question Number 67153 by mhmd last updated on 23/Aug/19 $${find}\:\int\left({v}^{\mathrm{3}} −\mathrm{2}\right)/\left({v}^{\mathrm{4}} +{v}\:\:\right){dv} \\ $$ Answered by mhmd last updated on 23/Aug/19 $$ \\ $$ Answered…
Question Number 1616 by 123456 last updated on 27/Aug/15 $$\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} \\…