Question Number 142338 by rs4089 last updated on 30/May/21 $$\int_{\mathrm{0}} ^{\infty} \frac{{sinx}}{{x}^{\mu} }{dx}\:\:=?\:\:\: \\ $$ Answered by Dwaipayan Shikari last updated on 30/May/21 $$\frac{\mathrm{1}}{{x}^{\mu} }=\frac{\mathrm{1}}{\Gamma\left(\mu\right)}\int_{\mathrm{0}}…
Question Number 142333 by mohammad17 last updated on 30/May/21 Commented by mohammad17 last updated on 30/May/21 $${please}\:{sir}\:{help}\:{me} \\ $$ Answered by Dwaipayan Shikari last updated…
Question Number 11263 by tawa last updated on 18/Mar/17 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}\:\mathrm{in}\:\mathrm{the}\:\mathrm{equation}\:. \\ $$$$\mathrm{625}^{\mathrm{x}\:−\:\mathrm{5}} \:=\:\mathrm{200}\sqrt{\mathrm{x}^{\mathrm{3}} } \\ $$ Answered by ajfour last updated on 18/Mar/17 $$\mathrm{5}^{\mathrm{4}\left(\mathrm{x}−\mathrm{5}\right)} \:=\:\mathrm{200x}^{\mathrm{3}/\mathrm{2}}…
Question Number 11262 by 786786AM last updated on 18/Mar/17 $$\mathrm{The}\:\mathrm{k}^{\mathrm{th}} \:\mathrm{term}\:\mathrm{of}\:\mathrm{a}\:\mathrm{sequence}\:\mathrm{is}\:\mathrm{K},\:\mathrm{the}\:\mathrm{m}^{\mathrm{th}} \:\mathrm{term}\:\mathrm{of}\:\:\mathrm{M}\:\mathrm{and}\:\mathrm{n}^{\mathrm{th}} \:\mathrm{term}\:\mathrm{is}\:\mathrm{N}.\:\mathrm{Show}\:\mathrm{that}\:\mathrm{if}\:\mathrm{it}\:\mathrm{is}\:\mathrm{a}\:\mathrm{geometic}, \\ $$$$\left(\mathrm{m}−\mathrm{n}\right)\:\mathrm{log}\:\mathrm{K}\:+\:\left(\mathrm{n}−\mathrm{k}\right)\:\mathrm{log}\:\mathrm{M}\:+\:\left(\mathrm{k}−\mathrm{m}\right)\:\mathrm{log}\:\mathrm{N}\:=\:\mathrm{0}.\: \\ $$ Answered by mrW1 last updated on 20/Mar/17 $${K}={a}\centerdot{q}^{{k}−\mathrm{1}}…
Question Number 11261 by 786786AM last updated on 18/Mar/17 $$\mathrm{The}\:\mathrm{n}^{\mathrm{th}} \:\mathrm{term}\:\mathrm{of}\:\mathrm{a}\:\mathrm{progression}\:\mathrm{is}\:\mathrm{np}+\mathrm{q}\:\mathrm{and}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{n}\:\mathrm{terms}\:\mathrm{is}\:\mathrm{denoted}\:\mathrm{by}\:\mathrm{S}_{\mathrm{n}} . \\ $$$$\mathrm{Given}\:\mathrm{that}\:\mathrm{the}\:\mathrm{6}^{\mathrm{th}} \:\mathrm{term}\:\mathrm{is}\:\mathrm{4}\:\mathrm{times}\:\mathrm{2}^{\mathrm{nd}} \:\mathrm{term}\:\mathrm{and}\:\mathrm{that}\:\mathrm{S}_{\mathrm{3}} \:=\mathrm{12},\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}. \\ $$$$\mathrm{Express}\:\mathrm{S}_{\mathrm{n}} \:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{n}. \\ $$ Terms of Service…
Question Number 142329 by HarshSahu last updated on 30/May/21 $$\:{lim}_{{x}\rightarrow\infty} \:\left(\frac{{x}!}{{x}^{{x}} }\right)^{\frac{\mathrm{1}}{{x}}} \\ $$ Answered by Dwaipayan Shikari last updated on 30/May/21 $$\left(\frac{{x}!}{{x}^{{x}} }\right)^{\frac{\mathrm{1}}{{x}}} ={y}…
Question Number 76794 by necxxx last updated on 30/Dec/19 $${Find}\:{the}\:{sum}\:{of} \\ $$$${x}\:+\:\frac{{x}}{\mathrm{1}+{x}}\:+\:\frac{{x}}{\left(\mathrm{1}+{x}\right)^{\mathrm{2}} }\:+\:\frac{{x}}{\left(\mathrm{1}+{x}\right)^{\mathrm{3}} }+….\:{for} \\ $$$$\mid\frac{\mathrm{1}}{\mathrm{1}+{x}}\mid<\mathrm{1} \\ $$ Commented by turbo msup by abdo last…
Question Number 11258 by uni last updated on 18/Mar/17 $${cos}\mathrm{65}={m}\:\:\Rightarrow\:{sin}\mathrm{40}=? \\ $$ Answered by ajfour last updated on 18/Mar/17 $$\mathrm{let}\:\mathrm{p}=\mathrm{sin}\:\mathrm{40}\:=\mathrm{cos}\:\mathrm{50} \\ $$$$\:\:\mathrm{p}\:=\mathrm{sin}\:\mathrm{40}=\:\mathrm{1}−\mathrm{2sin}\:^{\mathrm{2}} \mathrm{25} \\ $$$$\mathrm{sin}\:\mathrm{25}\:=\:\mathrm{cos}\:\mathrm{65}\:=\mathrm{m}…
Question Number 76793 by necxxx last updated on 30/Dec/19 $${The}\:{sum}\:{of}\:{the}\:{first}\:{n}\:{terms}\:{of}\:{a}\:{series} \\ $$$${is}\:{given}\:{by}:\:{S}_{{n}} ={n}^{\mathrm{2}} +\mathrm{7}{n}+\mathrm{2}. \\ $$$$\left({i}\right){Find}\:{a}\:{formula}\:{for}\:{the}\:{nth}\:{term} \\ $$$$\left({ii}\right){write}\:{down}\:{the}\:{first}\:\mathrm{5}\:{terms}\:{of}\:{the} \\ $$$${sequence} \\ $$$$ \\ $$ Commented…
Question Number 11256 by 786786AM last updated on 18/Mar/17 $$\mathrm{In}\:\mathrm{the}\:\mathrm{arithmetic}\:\mathrm{progression},\:\mathrm{u}_{\mathrm{1}\:} =\mathrm{1}.\mathrm{Given}\:\mathrm{that}\:\mathrm{u}_{\mathrm{7}\:} ,\:\mathrm{u}_{\mathrm{11}} \mathrm{and}\:\mathrm{u}_{\mathrm{17}} \:\mathrm{are}\:\mathrm{in}\:\mathrm{geometric}\: \\ $$$$\mathrm{progression},\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{each}. \\ $$ Answered by ajfour last updated on 18/Mar/17…