Question Number 69609 by TawaTawa last updated on 25/Sep/19 Commented by Prithwish sen last updated on 25/Sep/19 $$\mathrm{I}\:\mathrm{think} \\ $$$$\mathrm{The}\:\mathrm{area}\:\mathrm{of}\:\mathrm{inner}\:\mathrm{section}\:=\:\pi\left(\mathrm{75}\right)^{\mathrm{2}} \mathrm{sq}.\:\mathrm{cm} \\ $$$$\mathrm{The}\:\mathrm{area}\:\mathrm{of}\:\mathrm{outer}\:\mathrm{section}\:=\:\pi\left(\mathrm{100}−\mathrm{75}\right)\left(\mathrm{100}+\mathrm{75}\right) \\ $$$$=\:\pi×\mathrm{25}×\mathrm{175}\:\mathrm{sq}.\:\mathrm{cm}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…
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Question Number 4071 by Yozzii last updated on 27/Dec/15 Commented by Yozzii last updated on 27/Dec/15 $${Just}\:{sharing}\:{some}\:{problems}\:{I}\:{did} \\ $$$${today}. \\ $$ Terms of Service Privacy…
Question Number 69607 by malwaan last updated on 25/Sep/19 $$\boldsymbol{{without}}\:\boldsymbol{{using}}\:\boldsymbol{{lhospital}}\:\boldsymbol{{please}} \\ $$$$\boldsymbol{{prove}}\:\boldsymbol{{that}} \\ $$$$\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {\boldsymbol{{lim}}}\:\frac{\boldsymbol{{x}}−\boldsymbol{{sin}}\:\boldsymbol{{x}}}{\boldsymbol{{x}}^{\mathrm{3}} }\:=\:\frac{\mathrm{1}}{\mathrm{6}} \\ $$$$\boldsymbol{{I}}\:\boldsymbol{{want}}\:\boldsymbol{{every}}\:\boldsymbol{{method}} \\ $$$$\boldsymbol{{possible}}\:\boldsymbol{{because}}\:\boldsymbol{{someone}} \\ $$$$\boldsymbol{{challenge}}\:\boldsymbol{{me}}\: \\ $$ Commented…
Question Number 135143 by mnjuly1970 last updated on 10/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…..{nice}\:\:\:{calculus}… \\ $$$$\:\:\:\:\:\:\:\:{please}\:\:{calculate}:\downarrow\downarrow\downarrow \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\::::\:\:\boldsymbol{\phi}\overset{??} {=}\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{H}_{{n}} ^{\:^{\mathrm{2}} } }{{n}^{\mathrm{2}} }\:\: \\ $$$$\:\:\:\:\:\: \\ $$…
Question Number 4067 by Yozzii last updated on 27/Dec/15 Commented by Yozzii last updated on 27/Dec/15 $${I}\:{don}'{t}\:{know}\:{what}\:{to}\:{do}\:{for}\:{the}\:{last} \\ $$$${sentence}.\:{What}\:{equation}\:{satisfies} \\ $$$$\mathrm{2}{x}_{\mathrm{1}} +{x}_{\mathrm{2}} ?\: \\ $$…
Question Number 69603 by Mikael last updated on 25/Sep/19 $$\int\:{x}^{\mathrm{3}} {arcsinxdx} \\ $$ Answered by MJS last updated on 25/Sep/19 $$\mathrm{by}\:\mathrm{parts} \\ $$$$\int{u}'{v}={uv}−\int{uv}' \\ $$$${u}'={x}^{\mathrm{3}}…
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Question Number 69597 by ozodbek last updated on 25/Sep/19 Commented by mathmax by abdo last updated on 25/Sep/19 $${generally}\:{let}\:{find}\:{f}\left({a}\right)\:=\int\sqrt{{x}^{\mathrm{2}} +{a}^{\mathrm{2}} }{dx}\:\:{with}\:{a}>\mathrm{0} \\ $$$${changement}\:{x}\:={ash}\left({t}\right)\:{give}\:{f}\left({a}\right)=\int{ach}\left({t}\right){ach}\left({t}\right){dt} \\ $$$$={a}^{\mathrm{2}}…
Question Number 69594 by ahmadshahhimat775@gmail.com last updated on 25/Sep/19 Answered by MJS last updated on 25/Sep/19 $$\mathrm{2}\leqslant{n}\leqslant\mathrm{4}:\:\mathrm{2}^{{n}!} <\mathrm{2}^{{n}} ! \\ $$$$\mathrm{5}\leqslant{n}:\:\mathrm{2}^{{n}!} >\mathrm{2}^{{n}} ! \\ $$$$\mathrm{ln}\:\mathrm{2}^{{n}!}…