Question Number 7317 by lakshaysethi last updated on 24/Aug/16 $${Prove}\:{that}\:\left[\frac{{n}+\mathrm{1}}{\mathrm{2}}\right]+\left[\frac{{n}+\mathrm{2}}{\mathrm{4}}\right]+\left[\frac{{n}+\mathrm{4}}{\mathrm{8}}\right]+\left[\frac{{n}+\mathrm{8}}{\:\mathrm{16}}\right]+……..={n}. \\ $$$${Such}\:{that}\:\left[.\right]\:{denotes}\:{greatest}\:{integer}\:{function}\:{and}\:{n}\in{N}. \\ $$ Commented by FilupSmith last updated on 23/Aug/16 $${S}=\underset{{t}=\mathrm{1}} {\overset{\infty} {\sum}}\lceil\frac{{n}+\mathrm{2}^{{t}−\mathrm{1}} }{\mathrm{2}^{{t}}…
Question Number 7316 by rohit meena last updated on 23/Aug/16 $${x}−{y}\:{and}\:{y}−{x}\: \\ $$$${x}=\left\{−\mathrm{2},−\mathrm{1},\mathrm{0},\mathrm{2},\mathrm{5}\right\} \\ $$$${y}=\left\{\mathrm{0},\mathrm{5},\mathrm{7},\mathrm{8},\mathrm{10}\right\} \\ $$ Commented by Rasheed Soomro last updated on 23/Aug/16…
Question Number 138384 by mohammad17 last updated on 13/Apr/21 $${find}\:{the}\:{singular}\:{point}\: \\ $$$$ \\ $$$$\left(\mathrm{1}\right)\:\frac{{e}^{{z}} }{{z}^{\mathrm{2}} } \\ $$$$ \\ $$$$\left(\mathrm{2}\right)\frac{{sin}\left({z}\right)}{{z}} \\ $$$$ \\ $$$${help}\:{me}\:{sir} \\…
Question Number 7314 by Rasheed Soomro last updated on 23/Aug/16 Commented by Rasheed Soomro last updated on 23/Aug/16 $${Top}\:{and}\:{bottom}\:{of}\:{a}\:{solid}\:{are}\:{congruent}\:{circles}. \\ $$$${Above}\:{is}\:{the}\:{cross}-{section}\:{of}\:{the}\:{solid},\:{which}\: \\ $$$${is}\:{obtained}\:{by}\:{cutting}\:{the}\:{solid}\:{in}\:{two}\:{equal}\:{parts}. \\ $$$${Find}\:{out}\:{the}\:{volume}\:{of}\:{the}\:{solid}.…
Question Number 138386 by ajfour last updated on 13/Apr/21 Commented by ajfour last updated on 13/Apr/21 $${Find}\:{maximum}\:{area}\:{of}\:\bigtriangleup{ABC}. \\ $$ Answered by mr W last updated…
Question Number 138383 by henderson last updated on 12/Apr/21 $$\boldsymbol{\mathrm{hi}}\:! \\ $$$$\boldsymbol{\mathrm{for}}\:{a}_{\mathrm{0}} \:=\:\mathrm{1}\:\boldsymbol{\mathrm{and}}\:\forall\:{n}\:\geqslant\:\mathrm{1},\:{a}_{{n}} \:=\:\frac{\mathrm{1}}{{n}}\:\underset{{k}=\mathrm{0}} {\overset{\mathrm{n}−\mathrm{1}} {\sum}}\:\:\frac{{a}_{{k}} }{{n}−{k}}\:. \\ $$$$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}\:\forall\:{n}\:\geqslant\:\mathrm{0},\:\boldsymbol{\mathrm{we}}\:\boldsymbol{\mathrm{get}}\:\mathrm{0}\:\leqslant\:{a}_{{n}} \:\leqslant\:\mathrm{1}. \\ $$ Commented by mitica…
Question Number 138377 by mnjuly1970 last updated on 13/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:……\:{advanced}\:…\:…\:…\:{calculus}…… \\ $$$$\:\:\:{evaluate}:::: \\ $$$$\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{ln}\left({x}\right)}{\:\sqrt[{\mathrm{3}}]{{x}^{\mathrm{2}} }\:.\left(\mathrm{2}+{x}\right)}\:{dx}=?? \\ $$$$\:\: \\ $$ Terms of…
Question Number 138376 by KwesiDerek last updated on 12/Apr/21 $$\boldsymbol{\mathrm{log}}_{\mathrm{4}} \left(\boldsymbol{\mathrm{x}}+\mathrm{2}\right)+\boldsymbol{\mathrm{log}}_{\mathrm{3}} \left(\boldsymbol{\mathrm{x}}−\mathrm{2}\right)=\mathrm{1} \\ $$$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{x}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 138379 by physicstutes last updated on 12/Apr/21 Commented by physicstutes last updated on 12/Apr/21 $$\mathrm{the}\:\mathrm{figure}\:\mathrm{shows}\:\mathrm{a}\:\mathrm{couple}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{magnitude}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{moment}\:\mathrm{of}\:\mathrm{the}\:\mathrm{couple}. \\ $$ Commented by ajfour last…
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Question Number 138378 by Ñï= last updated on 12/Apr/21 $${I}\left({t},{s}\right)=\int_{\mathrm{0}} ^{\infty} {x}^{−{t}} \left(\mathrm{1}+{x}\right)^{−{s}} {dx}=\frac{\Gamma\left(\mathrm{1}−{t}\right)\Gamma\left({s}+{t}−\mathrm{1}\right)}{\Gamma\left({s}\right)} \\ $$$${I}\left({t},{s}\right)=\int_{\mathrm{0}} ^{\infty} {x}^{−{t}} \left(\mathrm{1}+{x}\right)^{−{s}} {dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:=\int_{\mathrm{0}} ^{\infty} {x}^{−{t}} \left(\mathrm{1}+{x}\right)^{{m}−{s}}…