Question Number 192338 by josemate19 last updated on 15/May/23 $${y}=\:\left(\frac{\left(\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left({x}+{h}\right)^{\mathrm{3}} −{x}^{\mathrm{3}} }{{h}}\right)\left(\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{x}^{{n}+\mathrm{1}} }{{n}+\mathrm{1}}\right)}{\int_{\mathrm{0}} ^{\:{x}} {lnt}\:{dt}}\right) \\ $$$$ \\ $$$$\frac{{dy}}{{dx}}? \\ $$ Answered…
Question Number 126801 by john_santu last updated on 24/Dec/20 $$\:\:\underset{{x}\rightarrow{a}} {\mathrm{lim}}\:\:\frac{{x}^{{a}} −{a}^{{x}} }{{a}^{{x}} −{a}^{{a}} }\:=\:\:;\:{a}>\mathrm{0}\: \\ $$$$\: \\ $$ Answered by liberty last updated on…
Question Number 61261 by Jmasanja last updated on 31/May/19 $${for}\:{polynomial}\:{p}\left({x}\right),{the}\:{value}\:{of}\: \\ $$$${p}\left(\mathrm{3}\right)\:{is}\:−\mathrm{2}.{which}\:{of}\:{the}\:{following}\: \\ $$$${must}\:{be}\:{true}\:{about}\:{p}\left({x}\right)? \\ $$$$\left({a}\right){x}−\mathrm{5}\:{is}\:{the}\:{factor}\:{of}\:{p}\left({x}\right) \\ $$$$\left({b}\right){x}−\mathrm{2}{is}\:{the}\:{factor}\:{of}\:{p}\left({x}\right) \\ $$$$\left({c}\right){x}+\mathrm{2}\:{is}\:{the}\:{factor}\:{of}\:{p}\left({x}\right) \\ $$$$\left({d}\right){the}\:{reminder}\:{when}\:\:{p}\left({x}\right)\:{is}\:{divide} \\ $$$${d}\:{by}\:{x}−\mathrm{3}\:{is}\:−\mathrm{2} \\…
Question Number 126795 by mathocean1 last updated on 24/Dec/20 $${N}\:{is}\:{a}\:{number}\:\in\:\mathbb{N}\:{which}\:{has}\:{three} \\ $$$${digits}\:{and}\:{written}\:{xyz}\:{in}\:{base}\:\mathrm{10}\: \\ $$$${such}\:{that}\:\begin{cases}{{xy}+{xz}+{yz}={xyz}}\\{\mathrm{0}<{x}<{y}<{z}}\end{cases} \\ $$$${Determinate}\:{N}. \\ $$ Commented by JDamian last updated on 24/Dec/20…
Question Number 61258 by cesar.marval.larez@gmail.com last updated on 31/May/19 $$\boldsymbol{{C}}{alculate},\:{using}\:{cartesian}\:{coodinates},\:{the}\:{following} \\ $$$${integrals}: \\ $$$$ \\ $$$$\left.\mathrm{1}\right)\:\int\int_{{D}} {dxdy}\:\:{being}\:\:{D}=\left\{\:\left({x},{y}\right)\in{R}^{\mathrm{2}} /\mathrm{0}\leqslant{x}\leqslant\frac{\mathrm{1}}{\mathrm{2}},{y}+{x}\leqslant\mathrm{1},{y}\geqslant\mathrm{0}\right\} \\ $$$$\left.\mathrm{2}\right)\:\int\int_{{D}} {x}^{\mathrm{3}} {ydxdy}\:\:{being}\:{D}=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\mathrm{0}\leqslant{x}\leqslant\frac{\mathrm{1}}{\mathrm{2}},{y}+{x}\leqslant\mathrm{1},{y}\geqslant\mathrm{0}\right\} \\ $$$$\left.\mathrm{3}\right)\:\int\int_{{D}}…
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Question Number 192325 by cherokeesay last updated on 14/May/23 Answered by a.lgnaoui last updated on 14/May/23 $$\boldsymbol{\mathrm{s}}\mathrm{urface}\:\boldsymbol{\mathrm{S}}=\frac{\mathrm{1}}{\mathrm{2}}\left(\boldsymbol{\mathrm{AB}}×\boldsymbol{\mathrm{BF}}\right)=\frac{\mathrm{1}}{\mathrm{2}}\boldsymbol{\mathrm{CD}}×\left(\boldsymbol{\mathrm{BD}}−\boldsymbol{\mathrm{DF}}\right) \\ $$$$\:\:\boldsymbol{\mathrm{S}}=\mathrm{2}\boldsymbol{\mathrm{CD}} \\ $$$$\boldsymbol{\mathrm{C}}\mathrm{alcul}\:\:\boldsymbol{\mathrm{CD}} \\ $$$$\bigtriangleup\mathrm{ACE}\:\:\measuredangle\mathrm{EAC}=\measuredangle\mathrm{DEF}=\boldsymbol{\theta} \\ $$$$\boldsymbol{\mathrm{C}}\mathrm{E}=\mathrm{AEsin}\:\theta\:\:\:\mathrm{cos}\:\theta=\frac{\mathrm{5}}{\mathrm{AE}}\Rightarrow\mathrm{AE}=\frac{\mathrm{5}}{\mathrm{cos}\:\theta}…
Question Number 126791 by BHOOPENDRA last updated on 24/Dec/20 $${yy}''−\left({y}'\right)^{\mathrm{2}} ={e}^{{ax}\:} \:{find}\:{genral}\:{solution}? \\ $$ Commented by BHOOPENDRA last updated on 24/Dec/20 $${help}\:{me}\:{out}\:{this}? \\ $$ Answered…
Question Number 126788 by john_santu last updated on 24/Dec/20 $$\:\sigma\:=\:\underset{\mathrm{0}} {\overset{\:\:\:\:\:\infty} {\int}}\sqrt{{x}}\:{e}^{−{x}/\mathrm{4}} \:{dx}\:=\:?\: \\ $$ Answered by Ar Brandon last updated on 24/Dec/20 $$\mathrm{x}=\mathrm{u}^{\mathrm{2}} \:\Rightarrow\:\mathrm{dx}=\mathrm{2udu}…