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3-boys-X-Y-and-Z-are-standing-3-metres-north-of-each-other-if-X-and-Z-are-both-1-5m-tall-and-Y-is-2m-tall-Find-a-the-bearing-from-each-of-the-boys-b-the-bearing-if-Y-moves-to-the-left-

Question Number 40054 by Rio Mike last updated on 15/Jul/18 $$\mathrm{3}\:{boys}\:{X},{Y},{and}\:{Z}\:{are}\:{standing} \\ $$$$\mathrm{3}\:{metres}\:{north}\:{of}\:{each}\:{other} \\ $$$${if}\:{X}\:{and}\:{Z}\:{are}\:{both}\:\mathrm{1}.\mathrm{5}{m}\:{tall} \\ $$$${and}\:{Y}\:{is}\:\mathrm{2}{m}\:{tall}. \\ $$$${Find} \\ $$$$\left.{a}\right)\:{the}\:{bearing}\:{from}\:{each}\:{of} \\ $$$${the}\:{boys} \\ $$$$\left.{b}\right)\:{the}\:{bearing}\:{if}\:{Y}\:{moves}…

Please-help-lim-x-x-1-e-x-1-1-lim-x-x-1-e-x-1-1-g-x-x-1-e-x-1-1-g-x-

Question Number 171107 by Kodjo last updated on 07/Jun/22 $${Please}\:{help} \\ $$$${li}\underset{{x}\rightarrow−\infty} {{m}}\left({x}−\mathrm{1}\right){e}^{{x}−\mathrm{1}} −\mathrm{1}=? \\ $$$${li}\underset{{x}\rightarrow+\infty} {{m}}\left({x}−\mathrm{1}\right){e}^{{x}−\mathrm{1}} −\mathrm{1}=? \\ $$$${g}\left({x}\right)=\left({x}−\mathrm{1}\right){e}^{{x}−\mathrm{1}} −\mathrm{1} \\ $$$${g}\left({x}\right)'=? \\ $$$$…

prove-that-n-0-n-2-2n-2-2-4n-2n-1-3-7-2-3-piG-G-Catalan-s-constant-

Question Number 171094 by amin96 last updated on 07/Jun/22 $$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}: \\ $$$$\boldsymbol{\Omega}=\underset{\boldsymbol{\mathrm{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\left(\frac{\left(\boldsymbol{\mathrm{n}}!\right)^{\mathrm{2}} }{\left(\mathrm{2}\boldsymbol{\mathrm{n}}\right)!}\right)^{\mathrm{2}} \frac{\mathrm{2}^{\mathrm{4}\boldsymbol{\mathrm{n}}} }{\left(\mathrm{2}\boldsymbol{\mathrm{n}}+\mathrm{1}\right)^{\mathrm{3}} }\overset{?} {=}\frac{\mathrm{7}}{\mathrm{2}}\boldsymbol{\zeta}\left(\mathrm{3}\right)−\pi\boldsymbol{\mathrm{G}} \\ $$$$\boldsymbol{\mathrm{G}}−\boldsymbol{\mathrm{Catalan}}'\boldsymbol{\mathrm{s}}\:\:\boldsymbol{\mathrm{constant}} \\ $$ Terms of…

lim-n-k-1-n-1-k-2-n-

Question Number 105498 by Dwaipayan Shikari last updated on 29/Jul/20 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\left(\frac{\mathrm{1}}{{k}}\right)\right)^{\frac{\mathrm{2}}{{n}}} \\ $$ Commented by JDamian last updated on 29/Jul/20 "From n=1 up to n"? -- Please, review your question Commented…

Question-171038

Question Number 171038 by Mastermind last updated on 06/Jun/22 Answered by MJS_new last updated on 07/Jun/22 $$\underset{\mathrm{4}} {\overset{\mathrm{9}} {\int}}\frac{{x}+\mathrm{1}}{{x}+\mathrm{2}\sqrt{{x}}−\mathrm{3}}{dx}=\underset{\mathrm{4}} {\overset{\mathrm{9}} {\int}}\frac{{x}+\mathrm{1}}{\left(\sqrt{{x}}+\mathrm{1}\right)^{\mathrm{2}} −\mathrm{4}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{{x}}+\mathrm{1}\:\rightarrow\:{dx}=\mathrm{2}\sqrt{{x}}{dt}\right] \\…

Question-171025

Question Number 171025 by Mastermind last updated on 06/Jun/22 Answered by greougoury555 last updated on 06/Jun/22 $$\left(\mathrm{1}\right)\:{x}\geqslant−\mathrm{3}\Rightarrow\frac{\mathrm{2}{x}+\mathrm{3}−{x}−\mathrm{2}}{{x}+\mathrm{2}}\:>\mathrm{0} \\ $$$$\:\Rightarrow\frac{{x}+\mathrm{1}}{{x}+\mathrm{2}}\:>\mathrm{0}\:;\:{x}<−\mathrm{2}\:\cup\:{x}>−\mathrm{1}\: \\ $$$$\:\therefore\:{solution}\::\:\left[−\mathrm{3},−\mathrm{2}\right)\:\cup\left(−\mathrm{1},\infty\right) \\ $$$$\left(\mathrm{2}\right)\:{x}<−\mathrm{3}\Rightarrow\frac{−\mathrm{3}−{x}−\mathrm{2}}{{x}+\mathrm{2}}\:>\mathrm{0} \\ $$$$\Rightarrow\:\frac{−{x}−\mathrm{5}}{{x}+\mathrm{2}}\:>\mathrm{0}\:;\:\frac{{x}+\mathrm{5}}{{x}+\mathrm{2}}\:<\mathrm{0}…