Question Number 203875 by MathedUp last updated on 31/Jan/24 $$\mathrm{Hmmm}…..\:\mathrm{I}\:\mathrm{have}\:\mathrm{one}\:\mathrm{Question}. \\ $$$${f}\left({t}\right)\in{C}^{\infty} \:,\:\left\{{C}_{\:} ^{\boldsymbol{\alpha}} \:\mathrm{mean}\:\mathrm{can}\:\mathrm{derivate}\:\boldsymbol{\alpha}\:\mathrm{times}.\right\} \\ $$$$\mathrm{where}\:{t}\in\mathbb{R}\:,\:\mathrm{Can}\:{f}\left({t}\right)\:\:\mathrm{integrable}\:\mathrm{when}\:{S}\in\mathbb{R}\backslash\left\{\mathbb{Q}\right\}?? \\ $$$$\mathrm{Ex}.\:\mathrm{integral}\:\int_{\mathrm{1}} ^{\:{e}} \:\mathrm{ln}\left({z}\right)\mathrm{d}{z}\:{S}\in\left[\mathrm{1},{e}\right]\: \\ $$$$\mathrm{But}\:\mathrm{Except}\:\mathbb{Q}\:\mathrm{in}\:\mathrm{set}\:{S}\:\mathrm{like}..\:{S}^{'} ={S}\backslash\left\{\mathbb{Q}\right\}\: \\…
Question Number 203867 by Mathspace last updated on 30/Jan/24 $${find}\:\int\sqrt{\frac{\mathrm{1}−{x}^{\mathrm{3}} }{\mathrm{1}+{x}^{\mathrm{3}} }}{dx} \\ $$ Answered by MathematicalUser2357 last updated on 06/Feb/24 $$\frac{\mathrm{8}{x}\sqrt{\frac{\mathrm{1}−{x}^{\mathrm{3}} }{{x}^{\mathrm{3}} +\mathrm{1}}}{F}_{\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{3}};−\frac{\mathrm{1}}{\mathrm{2}},\frac{\mathrm{1}}{\mathrm{2}};\frac{\mathrm{4}}{\mathrm{3}};{x}^{\mathrm{3}}…
Question Number 203858 by Mastermind last updated on 30/Jan/24 $$\mathrm{Classsify}\:\mathrm{the}\:\mathrm{critical}\:\mathrm{points}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function} \\ $$$$\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)\:=\:\mathrm{x}^{\mathrm{2}} \mathrm{y}\:+\:\frac{\mathrm{1}}{\mathrm{3}}\mathrm{y}^{\mathrm{3}} \:−\:\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{2} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{in}\:\mathrm{advance}! \\ $$ Commented…
Question Number 203859 by Mastermind last updated on 30/Jan/24 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{surface}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{z}\:=\:\mathrm{xy} \\ $$$$\mathrm{has}\:\mathrm{neither}\:\mathrm{a}\:\mathrm{maximum}\:\mathrm{nor}\:\mathrm{a}\:\mathrm{minimum}\:\mathrm{point} \\ $$ Commented by AST last updated on 30/Jan/24 $${For}\:{x},{y}\rightarrow\infty;\:{z}\rightarrow\infty \\…
Question Number 203846 by York12 last updated on 30/Jan/24 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\underset{{i}=\mathrm{2}} {\overset{{n}} {\prod}}\left(\frac{{i}^{\mathrm{2}} −\mathrm{1}}{{i}^{\mathrm{2}} }\right) \\ $$ Answered by MM42 last updated on 30/Jan/24 $${p}_{{n}}…
Question Number 203836 by patrice last updated on 29/Jan/24 Answered by Frix last updated on 30/Jan/24 $$\mathrm{In}\:\mathrm{3}\:\mathrm{steps}: \\ $$$$\mathrm{1}.\:{t}={x}^{\mathrm{2}} −\mathrm{1} \\ $$$$\mathrm{2}.\:{u}=\frac{\mathrm{5}{t}+\sqrt{\mathrm{25}{t}^{\mathrm{2}} +\mathrm{11}}}{\:\mathrm{11}} \\ $$$$\mathrm{3}.\:{v}=\frac{\sqrt{\mathrm{1}+{u}}}{\:\sqrt{\mathrm{1}−{u}}}\:\Rightarrow…
Question Number 203822 by 073 last updated on 29/Jan/24 Answered by esmaeil last updated on 29/Jan/24 $$\mathrm{1}:\frac{\mathrm{1}}{{x}}={p}\overset{{x}\rightarrow\infty\rightarrow{p}\rightarrow\mathrm{0}} {\rightarrow}\left[\frac{{x}+\mathrm{1}}{{x}}\right]=\left[{p}+\mathrm{1}\right)=\mathrm{1}\rightarrow \\ $$$$\Omega=\underset{{p}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{sinp}}{{p}}=\mathrm{1} \\ $$ Answered by…
Question Number 203832 by depressiveshrek last updated on 29/Jan/24 $$\mathrm{How}\:\mathrm{many}\:\mathrm{bit}\:\mathrm{strings}\:\mathrm{of}\:\mathrm{length}\:\mathrm{10}\:\mathrm{do}\:\mathrm{not} \\ $$$$\mathrm{have}\:\mathrm{four}\:\mathrm{consecutive}\:\mathrm{1s}? \\ $$ Answered by nikif99 last updated on 30/Jan/24 $${Total}\:{number}\:{of}\:{bit}\:{strings}\:{of}\:{length}\:\mathrm{10} \\ $$$${is}\:\mathrm{2}^{\mathrm{10}} =\mathrm{1024}\:\left(\mathrm{0}−\mathrm{1023}\right).…
Question Number 203833 by depressiveshrek last updated on 29/Jan/24 $$\mathrm{How}\:\mathrm{many}\:\mathrm{bit}\:\mathrm{strings}\:\mathrm{of}\:\mathrm{length}\:\mathrm{11}\:\mathrm{have} \\ $$$$\mathrm{exactly}\:\mathrm{three}\:\mathrm{consecutive}\:\mathrm{1s}? \\ $$ Answered by nikif99 last updated on 30/Jan/24 $${Such}\:{a}\:{typical}\:{bit}\:{string}\:{of}\:{length}=\mathrm{11}\:{is} \\ $$$$\mathrm{000}\underset{{pos}=\mathrm{4}} {\underbrace{\mathrm{111}}00000}…
Question Number 203835 by patrice last updated on 29/Jan/24 Answered by MathematicalUser2357 last updated on 30/Jan/24 $${bruh} \\ $$ Commented by Frix last updated on…