Question Number 121353 by john santu last updated on 06/Nov/20 Answered by liberty last updated on 07/Nov/20 $$\mathrm{Let}\:\mathrm{x}\:\mathrm{be}\:\mathrm{the}\:\mathrm{x}−\mathrm{coordinate}\:\mathrm{of}\:\mathrm{end}\:\mathrm{point}\: \\ $$$$\mathrm{that}\:\mathrm{lies}\:\mathrm{on}\:\mathrm{the}\:\mathrm{x}−\mathrm{axis}\:\mathrm{and}\:\mathrm{let}\:\mathrm{the}\:\mathrm{other} \\ $$$$\mathrm{endpoint}\:\mathrm{be}\:\left(\mathrm{0},\mathrm{y}\right).\:\mathrm{Thus}\:\mathrm{there}\:\mathrm{is}\:\mathrm{a}\:\mathrm{function} \\ $$$$\mathrm{f}\:\mathrm{which}\:\mathrm{gives}\:\mathrm{y}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{x}.\:\mathrm{Since} \\…
Question Number 121282 by mnjuly1970 last updated on 06/Nov/20 $$\:\:\:\:\:\:\:\:…\:\mathrm{advanced}\:\:\mathrm{mathematics}… \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\mathrm{prove}\:\:\mathrm{that}\:\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Psi=\int_{\mathrm{0}} ^{\:\mathrm{1}} \Gamma\left(\mathrm{2}−{x}\right)\Gamma\left(\mathrm{1}+{x}\right){dx}=\frac{\mathrm{7}}{\pi^{\mathrm{2}} }\:\zeta\left(\mathrm{3}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\mathrm{m}.\mathrm{n}.\mathrm{july}.\mathrm{1970}… \\ $$$$ \\ $$…
Question Number 121264 by benjo_mathlover last updated on 06/Nov/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{point}\:\mathrm{on}\:\mathrm{the}\:\mathrm{curve} \\ $$$$\mathrm{x}=\mathrm{2y}^{\mathrm{2}} \:\mathrm{closest}\:\mathrm{to}\:\mathrm{the}\:\mathrm{point} \\ $$$$\left(\mathrm{10},\mathrm{0}\right) \\ $$ Answered by liberty last updated on 06/Nov/20 $$\mathrm{Let}\:\mathrm{L}\:\mathrm{be}\:\mathrm{the}\:\mathrm{square}\:\mathrm{of}\:\mathrm{distance}\:\mathrm{between}…
Question Number 186752 by depressiveshrek last updated on 09/Feb/23 $$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\:\frac{\sqrt{{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} +\mathrm{7}}+\sqrt[{\mathrm{3}}]{{x}^{\mathrm{4}} +\mathrm{3}}}{\:\sqrt[{\mathrm{4}}]{{x}^{\mathrm{6}} +\mathrm{2}{x}^{\mathrm{5}} +\mathrm{1}}−\sqrt[{\mathrm{5}}]{{x}^{\mathrm{7}} +\mathrm{2}{x}^{\mathrm{3}} +\mathrm{3}}} \\ $$$${Please}\:{show}\:{work}. \\ $$ Answered by Ar…
Question Number 121202 by benjo_mathlover last updated on 05/Nov/20 Commented by liberty last updated on 05/Nov/20 $$\mathrm{g}\left(\mathrm{x}\right)=\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{x}−\mathrm{1}}{\mathrm{x}}\:=\:\mathrm{x}+\mathrm{1}−\frac{\mathrm{1}}{\mathrm{x}} \\ $$$$\mathrm{g}'\left(\mathrm{x}\right)=\mathrm{1}+\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\:>\:\mathrm{0}\:,\:\mathrm{g}\left(\mathrm{x}\right)\:\mathrm{increasing}\:\mathrm{both}\:\mathrm{sides} \\ $$$$\mathrm{interval}\:\left(−\infty,\mathrm{0}\right)\:\cup\left(\mathrm{0},\infty\right)\:.\:\mathrm{Then}\:\mathrm{g}\left(\mathrm{x}\right) \\ $$$$\mathrm{no}\:\mathrm{have}\:\mathrm{local}\:\mathrm{maxima}\:\mathrm{and}\:\mathrm{local}\:\mathrm{minima}…
Question Number 121097 by sdfg last updated on 05/Nov/20 Answered by TITA last updated on 05/Nov/20 $${is}\:{x}'=\frac{{dx}}{{dt}}\:? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 186473 by nadovic last updated on 04/Feb/23 $$\mathrm{A}\:\mathrm{metallic}\:\mathrm{cube}\:\mathrm{is}\:\mathrm{subjected}\:\mathrm{to} \\ $$$$\mathrm{heating}\:\mathrm{such}\:\mathrm{that}\:\mathrm{as}\:\mathrm{the}\:\mathrm{metal} \\ $$$$\mathrm{expands},\:\mathrm{the}\:\mathrm{total}\:\mathrm{surface}\:\mathrm{area} \\ $$$$\mathrm{increases}\:\mathrm{at}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{6}.\mathrm{25}\:\mathrm{cm}^{\mathrm{2}} \mathrm{s}^{−\mathrm{1}} . \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{rate}\:\mathrm{at}\:\mathrm{which}\:\mathrm{each} \\ $$$$\mathrm{side}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cube}\:\mathrm{is}\:\mathrm{increasing}\:\mathrm{when} \\ $$$$\mathrm{the}\:\mathrm{volume}\:\mathrm{is}\:\mathrm{51}.\mathrm{2}\:\mathrm{cm}^{\mathrm{3}} .…
Question Number 120912 by bemath last updated on 04/Nov/20 $$\:\mathrm{find}\:\frac{\mathrm{dy}}{\mathrm{dx}}\:\mathrm{from}\:\mathrm{equation}\: \\ $$$$\:\frac{\mathrm{xy}^{\mathrm{3}} }{\mathrm{sec}\:\mathrm{y}−\mathrm{3}}\:=\:\mathrm{1}+\mathrm{y}^{\mathrm{4}} \\ $$ Answered by liberty last updated on 04/Nov/20 $$\mathrm{by}\:\mathrm{implicit}\:\mathrm{differential}\: \\ $$$$\Rightarrow\:\frac{\mathrm{xy}^{\mathrm{3}}…
Question Number 186445 by myint last updated on 04/Feb/23 $$\mathrm{Show}\:\:\mathrm{that}\:\:\mathrm{the}\:\:\mathrm{function}\:\:\mathrm{y}\:=\:\:\mid\:\mathrm{x}\:−\mathrm{5}\:\mid\:\:\mathrm{has}\:\:\mathrm{no}\:\:\mathrm{derivative}\:\:\mathrm{at}\:\:\mathrm{x}\:\:=\:\mathrm{5}. \\ $$ Answered by ARUNG_Brandon_MBU last updated on 04/Feb/23 $${f}\:'\left(\mathrm{5}\right)=\underset{{x}\rightarrow\mathrm{5}} {\mathrm{lim}}\frac{{f}\left({x}\right)−{f}\left(\mathrm{5}\right)}{{x}−\mathrm{5}}=\underset{{x}\rightarrow\mathrm{5}} {\mathrm{lim}}\frac{\mid{x}−\mathrm{5}\mid}{{x}−\mathrm{5}} \\ $$$$\underset{{x}\rightarrow\mathrm{5}^{>} }…
Question Number 120593 by snipers237 last updated on 01/Nov/20 $$ \\ $$$$\:\underset{{z}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\Gamma\left({z}\right)+\Gamma\left(−{z}\right)}{\mathrm{2}}\:\overset{?} {=}\:−\gamma \\ $$ Answered by mnjuly1970 last updated on 02/Nov/20 $${solution}: \\…