Question Number 199531 by SANOGO last updated on 04/Nov/23 $$\int_{{o}} ^{+{oo}} {ln}\left({atan}\left({x}\right){dx}\:\right. \\ $$ Answered by Frix last updated on 05/Nov/23 $$\mathrm{Doesn}'\mathrm{t}\:\mathrm{converge}. \\ $$ Terms…
Question Number 199467 by Calculusboy last updated on 04/Nov/23 Answered by cortano12 last updated on 04/Nov/23 $$\:\mathrm{4}\:=\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left(\mathrm{a}−\mathrm{2}\right)\mathrm{x}^{\mathrm{3}} +\left(\mathrm{3}+\mathrm{c}\right)\mathrm{x}^{\mathrm{2}} +\left(\mathrm{b}−\mathrm{3}\right)\mathrm{x}+\mathrm{2}+\mathrm{d}}{\mathrm{x}^{\mathrm{2}} \:\left[\sqrt{\mathrm{1}+\frac{\mathrm{a}}{\mathrm{x}}+\frac{\mathrm{3}}{\mathrm{x}^{\mathrm{2}} }+\frac{\mathrm{b}}{\mathrm{x}^{\mathrm{3}} }+\frac{\mathrm{2}}{\mathrm{x}^{\mathrm{4}} }}\:+\sqrt{\mathrm{1}+\frac{\mathrm{2}}{\mathrm{x}}−\frac{\mathrm{c}}{\mathrm{x}^{\mathrm{2}} }+\frac{\mathrm{3}}{\mathrm{x}^{\mathrm{3}}…
Question Number 199520 by tri26112004 last updated on 04/Nov/23 $${n}^{\mathrm{4}} +{an}^{\mathrm{3}} +{bn}^{\mathrm{2}} +{cn}+{d}={k}^{\mathrm{2}} \:\left({k}\in{N}\right) \\ $$$${a},{b},{c},{d}=¿ \\ $$ Answered by Frix last updated on 04/Nov/23…
Question Number 199522 by cherokeesay last updated on 04/Nov/23 Answered by cortano12 last updated on 05/Nov/23 $$\left(\mathrm{g}_{\mathrm{1}} \right)\:\equiv\:\mathrm{y}=\mathrm{ax}+\mathrm{b}\:\left(\mathrm{tangent}\:\mathrm{line}\:\right) \\ $$$$\:\mathrm{where}\:\mathrm{a}\:=\:\frac{\mathrm{1}}{\mathrm{4}\left(\frac{\mathrm{1}}{\mathrm{4}}\right)}\:=\:\mathrm{1} \\ $$$$\:\mathrm{and}\:\mathrm{b}\:=\:\frac{\mathrm{1}}{\mathrm{4}}−\frac{\mathrm{1}}{\mathrm{8}}=\frac{\mathrm{1}}{\mathrm{8}} \\ $$$$\:\:\therefore\:\mathrm{y}=\mathrm{x}+\frac{\mathrm{1}}{\mathrm{8}} \\…
Question Number 199509 by hardmath last updated on 04/Nov/23 Commented by York12 last updated on 04/Nov/23 Commented by York12 last updated on 04/Nov/23 $$\mathrm{That}\:\mathrm{is}\:\mathrm{more}\:\mathrm{general}\: \\…
Question Number 199510 by universe last updated on 04/Nov/23 Answered by mr W last updated on 06/Nov/23 Commented by mr W last updated on 06/Nov/23…
Question Number 199511 by SANOGO last updated on 04/Nov/23 $$\int_{\mathrm{1}} ^{+{oo}} {ln}\left(\mathrm{1}+{lnx}\right)^{−{lnx}} \:{dx} \\ $$ Commented by SANOGO last updated on 04/Nov/23 $${thank}\:{you} \\ $$…
Question Number 199498 by ajfour last updated on 04/Nov/23 Commented by ajfour last updated on 04/Nov/23 $${Outer}\:\bigtriangleup\:{is}\:{right}\:{angled}.\:{Given}\:{p},\: \\ $$$${determine}\:{q}\:{in}\:{terms}\:{of}\:{p}. \\ $$ Answered by ajfour last…
Question Number 199451 by hardmath last updated on 03/Nov/23 $$\mathrm{Find}: \\ $$$$\mathrm{1}.\:\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\sqrt[{\mathrm{5}\boldsymbol{\mathrm{n}}}]{\frac{\mathrm{5n}\:−\:\mathrm{25}}{\mathrm{3n}\:+\:\mathrm{15}}} \\ $$$$\mathrm{2}.\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\infty} {\mathrm{lim}}\:\left(\sqrt[{\mathrm{3}}]{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{3x}^{\mathrm{2}} \:+\:\mathrm{1}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{x}^{\mathrm{3}} \:−\:\mathrm{3x}^{\mathrm{2}} \:+\:\mathrm{1}}\:\right) \\ $$$$\mathrm{3}.\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\mathrm{4x}^{\mathrm{3}} \:−\:\mathrm{1}}{\mathrm{sin}^{\mathrm{6}} \:\mathrm{2x}}…
Question Number 199413 by universe last updated on 03/Nov/23 Answered by ajfour last updated on 03/Nov/23 $${b}\mathrm{cos}\:\alpha={R} \\ $$$$\left\{{R}\mathrm{tan}\:\alpha+\left(\frac{{a}}{{b}}\right){R}\right\}^{\mathrm{2}} +\left\{\left(\frac{{a}}{{b}}\right){R}\mathrm{tan}\:\alpha\right\}^{\mathrm{2}} ={R}^{\mathrm{2}} \\ $$$${say}\:\:\:\mathrm{tan}\:\alpha={t} \\ $$$$\Rightarrow\:{t}^{\mathrm{2}}…