Question Number 199466 by Calculusboy last updated on 04/Nov/23 Answered by Frix last updated on 04/Nov/23 $$\mathrm{Again}\:\mathrm{obvious}\:\mathrm{if}\:\mathrm{you}\:\mathrm{use}\:\mathrm{your}\:\mathrm{brain}: \\ $$$${x}=\mathrm{0} \\ $$ Terms of Service Privacy…
Question Number 199509 by hardmath last updated on 04/Nov/23 Commented by York12 last updated on 04/Nov/23 Commented by York12 last updated on 04/Nov/23 $$\mathrm{That}\:\mathrm{is}\:\mathrm{more}\:\mathrm{general}\: \\…
Question Number 199451 by hardmath last updated on 03/Nov/23 $$\mathrm{Find}: \\ $$$$\mathrm{1}.\:\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\sqrt[{\mathrm{5}\boldsymbol{\mathrm{n}}}]{\frac{\mathrm{5n}\:−\:\mathrm{25}}{\mathrm{3n}\:+\:\mathrm{15}}} \\ $$$$\mathrm{2}.\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\infty} {\mathrm{lim}}\:\left(\sqrt[{\mathrm{3}}]{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{3x}^{\mathrm{2}} \:+\:\mathrm{1}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{x}^{\mathrm{3}} \:−\:\mathrm{3x}^{\mathrm{2}} \:+\:\mathrm{1}}\:\right) \\ $$$$\mathrm{3}.\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\mathrm{4x}^{\mathrm{3}} \:−\:\mathrm{1}}{\mathrm{sin}^{\mathrm{6}} \:\mathrm{2x}}…
Question Number 199447 by jabarsing last updated on 03/Nov/23 $${b}_{{n}} ={sin}\left({a}_{\mathrm{1}} +\left({n}−\mathrm{1}\right){d}\right)\Rightarrow\:{S}_{{n}} =? \\ $$ Answered by aleks041103 last updated on 03/Nov/23 $${b}_{{n}} ={Im}\left({e}^{{i}\left({a}_{\mathrm{1}} +\left({n}−\mathrm{1}\right){d}\right)}…
Question Number 199432 by mr W last updated on 03/Nov/23 $${without}\:{using}\:{calculator}: \\ $$$${what}\:{is}\:{larger}?\:\mathrm{log}_{\mathrm{2}} \:\mathrm{3}\:{or}\:\mathrm{log}_{\mathrm{3}} \:\mathrm{5}? \\ $$ Answered by witcher3 last updated on 03/Nov/23 $$\frac{\mathrm{ln}\left(\mathrm{3}\right)}{\mathrm{ln}\left(\mathrm{2}\right)},\frac{\mathrm{ln}\left(\mathrm{5}\right)}{\mathrm{ln}\left(\mathrm{3}\right)}…
Question Number 199458 by Calculusboy last updated on 03/Nov/23 $$\boldsymbol{{Solve}}:\:\boldsymbol{{log}}_{\mathrm{3}} \boldsymbol{{p}}\:+\:\boldsymbol{{log}}_{\boldsymbol{{r}}} \mathrm{8}\:=\mathrm{5} \\ $$$$\boldsymbol{{r}}+\boldsymbol{{p}}=\mathrm{11}.\:\:\boldsymbol{{find}}\:\boldsymbol{{r\&p}} \\ $$ Answered by Frix last updated on 04/Nov/23 $$\mathrm{Obviously}\:{p}=\mathrm{9}\wedge{r}=\mathrm{2} \\…
Question Number 199389 by depressiveshrek last updated on 02/Nov/23 $$\mathrm{log}_{\mathrm{12}} \mathrm{60}=? \\ $$$$\mathrm{log}_{\mathrm{6}} \mathrm{30}={a} \\ $$$$\mathrm{log}_{\mathrm{15}} \mathrm{24}={b} \\ $$ Answered by cortano12 last updated on…
Question Number 199385 by hardmath last updated on 02/Nov/23 $$\mathrm{Find}: \\ $$$$\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\mathrm{x}^{\mathrm{15}} \:\sqrt{\mathrm{1}\:+\:\mathrm{3x}^{\mathrm{8}} }\:\mathrm{dx}\:=\:? \\ $$ Answered by witcher3 last updated on 02/Nov/23…
Question Number 199381 by Mingma last updated on 02/Nov/23 Answered by witcher3 last updated on 02/Nov/23 $$\left(\mathrm{202}\right)=\mathrm{2}.\mathrm{101} \\ $$$$\frac{\left(\mathrm{201}\right)!}{\mathrm{k}}\equiv\mathrm{0}\left[\mathrm{202}\right]\mathrm{0},\forall\mathrm{k}\in\left\{\mathrm{1},……\mathrm{201}\right)−\left\{\mathrm{2},\mathrm{101}\right) \\ $$$$\mathrm{J}\equiv\frac{\mathrm{201}!}{\mathrm{101}}+\frac{\mathrm{201}!}{\mathrm{2}}\left[\mathrm{202}\right] \\ $$$$\frac{\mathrm{201}!}{\mathrm{2}}=\mathrm{202}.\mathrm{3}.\mathrm{2}.\underset{\mathrm{k}=\mathrm{5},\mathrm{k}\neq\mathrm{101}} {\overset{\mathrm{201}} {\prod}}\mathrm{k}\equiv\mathrm{0}\left[\mathrm{202}\right]…
Question Number 199355 by hardmath last updated on 01/Nov/23 Answered by MathematicalUser2357 last updated on 04/Nov/23 $$\Omega\approx\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{{n}!}{{n}^{{n}} }\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}^{\mathrm{2}{n}} }??? \\ $$ Terms…