Question Number 188387 by cortano12 last updated on 28/Feb/23 Answered by Frix last updated on 28/Feb/23 $$\mathrm{I}\:\mathrm{think}\:\mathrm{because}\:\mathrm{of}\:\mathrm{symmetry}\:{a}={b}={c}=\mathrm{1}\:\Rightarrow \\ $$$$\mathrm{Minimum}\:\mathrm{is}\:\frac{\mathrm{3}}{\mathrm{2}} \\ $$ Answered by mnjuly1970 last…
Question Number 122704 by mnjuly1970 last updated on 19/Nov/20 $$\:\:\:\:\:\:\:\:\:\:\:…\:{general}\:\:{calculus}… \\ $$$$\:{i}:\:\:\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}−\mathrm{4}{x}}}\:\overset{??} {=}\underset{{n}=\mathrm{0}\:} {\overset{\infty} {\sum}}\left[\begin{pmatrix}{\mathrm{2}{n}}\\{\:{n}}\end{pmatrix}\:\:{x}^{{n}} \right] \\ $$$$\:{ii}:\:\frac{\pi}{\mathrm{2}}\:\overset{?} {=}\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left[\frac{\begin{pmatrix}{\mathrm{2}{n}}\\{\:{n}}\end{pmatrix}}{\mathrm{4}^{{n}} }\:\frac{\mathrm{1}}{\left(\mathrm{2}{n}+\mathrm{1}\right)}\right] \\ $$$$\:\:\:\:\:\:\:\:\:\: \\…
Question Number 122695 by liberty last updated on 19/Nov/20 $${Find}\:{maximum}\:{and}\:{minimum}\:{values} \\ $$$${of}\:{f}\left({x},{y}\right)\:=\:{xy}\:{on}\:{the}\:{circle}\:{g}\left({x},{y}\right)= \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{1}=\mathrm{0}\:. \\ $$ Answered by john santu last updated on…
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Question Number 57084 by frimpshaddie last updated on 30/Mar/19 Commented by Kunal12588 last updated on 30/Mar/19 $$\left({d}\right)\:{when}\:{the}\:{velocity}\:{of}\:{particle}\:{becomes}\:\mathrm{0} \\ $$$${then}\:{the}\:{particle}\:{is}\:{said}\:{to}\:{be}\:{in}\:{rest} \\ $$$$\left({horizontal}\:{motion}\:{only}\right) \\ $$$$\therefore{v}=\mathrm{0} \\ $$$$\Rightarrow\mathrm{3}{t}^{\mathrm{2}}…
Question Number 57012 by rahul 19 last updated on 28/Mar/19 $${Find}\:{the}\:{local}\:{minimum}\:{value}\:{of}\:{f}\left({x}\right) \\ $$$${where}\:{f}\left({x}\right)=\:\left({x}−\frac{\mathrm{1}}{{x}}\right)+\left(\frac{\mathrm{2}}{{x}−\frac{\mathrm{1}}{{x}}}\right)\:? \\ $$ Answered by mr W last updated on 29/Mar/19 $${let}\:{t}={x}−\frac{\mathrm{1}}{{x}} \\…
Question Number 188083 by Kalebwizeman last updated on 25/Feb/23 $${determine}\:{the}\:{value}\:{of}\:{b}\:{for}\:{which}\: \\ $$$$\:\:\:{y}=\frac{−{x}}{\mathrm{3}}\:+{b}\:\:{meets}\:{the}\:{graph}\:{of} \\ $$$$\:{y}^{\mathrm{2}} ={x}^{\mathrm{3}} \:\:{orthogonally} \\ $$ Commented by a.lgnaoui last updated on 27/Feb/23…
Question Number 122525 by mnjuly1970 last updated on 17/Nov/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{nice}\:\:{calculus}… \\ $$$$\:\:{prove}\:{that}\:\:\::::::\gg\:\:\:\Psi=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left(\mathrm{1}−{x}\right)}{\mathrm{2}−{x}}{dx}=−\frac{\pi^{\mathrm{2}} }{\mathrm{12}}\:\checkmark \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:…\:{m}.{n}.\mathrm{1970}… \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\: \\ $$ Answered by Dwaipayan Shikari…
Question Number 188037 by Michaelfaraday last updated on 25/Feb/23 $${find}\:\frac{{dy}}{{dx}} \\ $$$${y}=\mathrm{2}{x}^{\sqrt{{x}}} \\ $$ Answered by horsebrand11 last updated on 25/Feb/23 $$\:\mathrm{ln}\:{y}=\sqrt{{x}}\:\mathrm{ln}\:\left(\mathrm{2}{x}\right) \\ $$$$\:\frac{\mathrm{1}}{{y}}.{y}'=\frac{\mathrm{ln}\:\left(\mathrm{2}{x}\right)}{\mathrm{2}\sqrt{{x}}}+\frac{\mathrm{2}\sqrt{{x}}}{\mathrm{2}{x}} \\…
Question Number 188033 by Michaelfaraday last updated on 25/Feb/23 $${from}\:{first}\:{principle} \\ $$$${y}={xInx}\:\:{find}\:\frac{{dy}}{{dx}} \\ $$ Answered by a.lgnaoui last updated on 25/Feb/23 $$\frac{{dy}}{{dx}}={lnx}+\mathrm{1}=\frac{{y}}{{x}}+\mathrm{1} \\ $$$$\frac{{y}}{{x}}=\frac{{dy}}{{dx}}−\mathrm{1}\Rightarrow \\…