Question Number 84543 by niroj last updated on 14/Mar/20 $$\boldsymbol{\mathrm{Determine}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}}\:,\boldsymbol{\mathrm{c}}\:\:\boldsymbol{\mathrm{so}}\:\boldsymbol{\mathrm{that}} \\ $$$$\:\:\underset{\mathrm{x}\rightarrow\mathrm{0}} {\overset{\mathrm{lim}} {\:}}\:\frac{\left(\boldsymbol{\mathrm{a}}\:+\boldsymbol{\mathrm{b}}\:\mathrm{cos}\:\mathrm{x}\right)\:\mathrm{x}−\boldsymbol{\mathrm{c}}\:\mathrm{sin}\:\mathrm{x}}{\mathrm{x}^{\mathrm{5}} }=\mathrm{1} \\ $$ Commented by mr W last updated on 14/Mar/20…
Question Number 150079 by puissant last updated on 09/Aug/21 $$\int\frac{{dx}}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Answered by Ar Brandon last updated on 09/Aug/21 $$\int\frac{{dx}}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{2}} }=\frac{{px}+{q}}{{x}^{\mathrm{2}}…
Question Number 19002 by tawa tawa last updated on 02/Aug/17 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{number}\:\mathrm{of}\:\:\mathrm{time}\:\mathrm{three}\:\mathrm{divides}\:\mathrm{333}^{\mathrm{505}} \\ $$ Answered by RasheedSindhi last updated on 03/Aug/17 $$\mathrm{333}=\mathrm{37}×\mathrm{3}^{\mathrm{2}} \\ $$$$\mathrm{333}^{\mathrm{505}} =\mathrm{37}^{\mathrm{505}} ×\left(\mathrm{3}^{\mathrm{2}}…
Question Number 84532 by john santu last updated on 14/Mar/20 $$\mathrm{x}>\:\mathrm{0}\:,\:\mathrm{y}\:>\:\mathrm{0}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{xy}}{\mathrm{x}+\mathrm{y}}\:<\:\mathrm{x} \\ $$ Commented by mr W last updated on 14/Mar/20 $$\Rightarrow{y}<{x}+{y} \\…
Question Number 150064 by n0y0n last updated on 09/Aug/21 $$\mathrm{How}\:\mathrm{can}\:\mathrm{i}\:\mathrm{evaluate}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\: \\ $$$$\:\:\int_{\mathrm{2}} ^{\:\mathrm{4}} \frac{\mathrm{e}^{\mathrm{t}} }{\mathrm{t}}\mathrm{dt}\:=\:? \\ $$ Answered by Ar Brandon last updated…
Question Number 84531 by jagoll last updated on 14/Mar/20 $$\mathrm{find}\:\mathrm{for}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{image}\:\mathrm{ellipse} \\ $$$$\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{9}}\:+\:\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{8}}\:=\:\mathrm{1}\:\mathrm{if}\:\mathrm{reflected}\:\mathrm{with}\:\mathrm{line} \\ $$$$\mathrm{x}\:+\:\mathrm{y}\:=\:−\mathrm{4} \\ $$ Commented by jagoll last updated on 14/Mar/20…
Question Number 84528 by mr.perfected last updated on 14/Mar/20 $$\mathrm{1}=\mathrm{2} \\ $$ Commented by jagoll last updated on 14/Mar/20 $$\mathrm{one}\:\mathrm{man}\:\mathrm{have}\:\mathrm{2}\:\mathrm{wife} \\ $$$$\mathrm{haha} \\ $$ Commented…
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Question Number 150062 by 0731619 last updated on 09/Aug/21 Answered by Ar Brandon last updated on 09/Aug/21 $${li}_{\mathrm{2}} \left({x}\right)\underset{{function}} {\overset{{dilogarithm}} {=}}\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{x}^{{n}} }{{n}^{\mathrm{2}} }=−\int_{\mathrm{0}}…
Question Number 150056 by ajfour last updated on 09/Aug/21 Commented by ajfour last updated on 09/Aug/21 $${If}\:{the}\:{blue}\:{region}\:{is}\:{a}\:{square} \\ $$$${of}\:{maximum}\:{area},\:{find}\:{a} \\ $$$${and}\:{side}\:{s}\:{of}\:{the}\:{square}.\:\:\: \\ $$ Answered by…