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Author: Tinku Tara

calculate-0-1-x-1-x-dx-

Question Number 204902 by pticantor last updated on 01/Mar/24 $$\boldsymbol{{calculate}}\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\boldsymbol{{x}}\left(\mathrm{1}−\boldsymbol{{x}}\right)}\boldsymbol{{dx}} \\ $$ Answered by witcher3 last updated on 01/Mar/24 $$\mathrm{y}^{\mathrm{2}} +\mathrm{x}^{\mathrm{2}} −\mathrm{x}=\mathrm{0}\Leftrightarrow\mathrm{y}^{\mathrm{2}} +\left(\mathrm{x}−\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}}…

lim-n-n-e-x-n-where-x-n-1-1-1-1-2-1-n-

Question Number 204879 by universe last updated on 09/Aug/24 $$\:\:\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{n}!\left({e}−\mathrm{x}_{\mathrm{n}} \right)\:=\:? \\ $$$$\:\:\mathrm{where}\:\mathrm{x}_{\mathrm{n}\:} =\:\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}!}+\frac{\mathrm{1}}{\mathrm{2}!}+…+\frac{\mathrm{1}}{\mathrm{n}!} \\ $$ Commented by mr W last updated on 01/Mar/24…

The-figure-below-represents-a-design-on-the-windows-of-a-building-The-curved-part-XY-is-an-arc-of-a-circle-The-rise-of-the-segmental-arc-is-10cm-its-span-is-100cm-and-XZ-ZY-120cm-calculate-i-th

Question Number 204873 by necx122 last updated on 29/Feb/24 $${The}\:{figure}\:{below}\:{represents}\:{a}\:{design} \\ $$$${on}\:{the}\:{windows}\:{of}\:{a}\:{building}.\:{The} \\ $$$${curved}\:{part}\:{XY}\:{is}\:{an}\:{arc}\:{of}\:{a}\:{circle}. \\ $$$${The}\:{rise}\:{of}\:{the}\:{segmental}\:{arc}\:{is}\:\mathrm{10}{cm}, \\ $$$${its}\:{span}\:{is}\:\mathrm{100}{cm}\:{and}\:{XZ}={ZY}=\mathrm{120}{cm}. \\ $$$${calculate}: \\ $$$$\left({i}\right)\:{the}\:{radius}\:{of}\:{the}\:{circle} \\ $$$$\left({ii}\right)\:{the}\:{area}\:{of}\:{the}\:{segmental}\:{cap}, \\…

How-many-distinct-positive-integer-valued-solution-exist-the-equation-x-2-7x-11-x-2-13x-42-1-a-2-b-4-c-6-

Question Number 204869 by BaliramKumar last updated on 29/Feb/24 $$\mathrm{How}\:\mathrm{many}\:\mathrm{distinct}\:\mathrm{positive}\:\mathrm{integer}\:\mathrm{valued}\:\mathrm{solution}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\mathrm{exist}\:\mathrm{the}\:\mathrm{equation}\:\left({x}^{\mathrm{2}} \:−\:\mathrm{7}{x}\:+\:\mathrm{11}\right)^{\left({x}^{\mathrm{2}} \:−\mathrm{13}{x}\:+\:\mathrm{42}\right)} \:=\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{2}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{4}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{6}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{d}\right)\:\mathrm{8} \\ $$ Answered by A5T last updated on…

f-x-1-log-2x-5-x-1-2-Find-the-domain-of-this-function-

Question Number 204853 by depressiveshrek last updated on 29/Feb/24 $${f}\left({x}\right)=\sqrt{\mathrm{1}−\mathrm{log}_{\left(\mathrm{2}{x}+\mathrm{5}\right)} \left(\left({x}+\mathrm{1}\right)^{\mathrm{2}} \right)} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{domain}\:\mathrm{of}\:\mathrm{this}\:\mathrm{function} \\ $$ Answered by Frix last updated on 29/Feb/24 $$−\frac{\mathrm{5}}{\mathrm{2}}<{x}\leqslant\mathrm{2}\wedge{x}\neq−\mathrm{2}\wedge{x}\neq−\mathrm{1} \\…

x-3-x-2-2x-3-dx-

Question Number 204866 by mathlove last updated on 29/Feb/24 $$\int\:\frac{{x}+\mathrm{3}}{{x}^{\mathrm{2}} \sqrt{\mathrm{2}{x}+\mathrm{3}}}\:{dx}=? \\ $$ Answered by Frix last updated on 29/Feb/24 $$\int\frac{{x}+\mathrm{3}}{{x}^{\mathrm{2}} \sqrt{\mathrm{2}{x}+\mathrm{3}}}{dx}\:\overset{{t}=\frac{\sqrt{\mathrm{2}{x}+\mathrm{3}}}{{x}}} {=}−\int{dt}=−{t}=−\frac{\sqrt{\mathrm{2}{x}+\mathrm{3}}}{{x}}+{C} \\ $$…