Question Number 65961 by mmkkmm000m last updated on 06/Aug/19 $$\mathrm{Let}\:\frac{{d}}{{dx}}\left({F}\left({x}\right)\right)\:=\:\frac{{e}^{\mathrm{sin}\:{x}} }{{x}}\:,\:{x}>\mathrm{0}. \\ $$$$\mathrm{If}\:\underset{\:\mathrm{1}} {\overset{\mathrm{4}} {\int}}\:\:\frac{\mathrm{2}\:{e}^{\mathrm{sin}\:{x}^{\mathrm{2}} } }{{x}}\:{dx}\:=\:{F}\left({k}\right)−{F}\left(\mathrm{1}\right),\:\mathrm{then}\:\mathrm{one} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:\:{k}\:\:\mathrm{is} \\ $$ Answered by mr W…
Question Number 131429 by mathlove last updated on 04/Feb/21 $${if}\:\:\:\:\frac{{aa}−{bb}}{{ab}+{ba}}=\frac{\mathrm{1}}{\mathrm{7}}\:\:\:\:\:\:\:\:\:{then}\:{faind}\:\frac{{a}}{{b}}=? \\ $$ Answered by Dwaipayan Shikari last updated on 04/Feb/21 $$\frac{{a}^{\mathrm{2}} −{b}^{\mathrm{2}} }{\mathrm{2}{ab}}=\frac{\mathrm{1}}{\mathrm{7}}\Rightarrow\left(\frac{{a}}{{b}}\right)−\left(\frac{{b}}{{a}}\right)=\frac{\mathrm{2}}{\mathrm{7}}\Rightarrow\frac{{a}}{{b}}=\frac{−\frac{\mathrm{2}}{\mathrm{7}}\pm\sqrt{\frac{\mathrm{4}}{\mathrm{49}}+\mathrm{4}}}{\mathrm{2}} \\ $$$$=\frac{−\mathrm{1}\pm\mathrm{5}\sqrt{\mathrm{2}}}{\mathrm{7}}…
Question Number 131428 by pticantor last updated on 04/Feb/21 $$\:\boldsymbol{{S}}=\underset{\boldsymbol{{n}}\geqslant\mathrm{1}} {\sum}\frac{\mathrm{6}}{\boldsymbol{{n}}\left(\boldsymbol{{n}}+\mathrm{1}\right)\left(\mathrm{2}\boldsymbol{{n}}+\mathrm{1}\right)} \\ $$$$\left.\mathrm{1}\right)\:\boldsymbol{{show}}\:\boldsymbol{{that}}\:\boldsymbol{{S}}\:\boldsymbol{{converges}} \\ $$$$\left.\mathrm{2}\right)\:\boldsymbol{{give}}\:\boldsymbol{{the}}\:\boldsymbol{{value}}\:\boldsymbol{{of}}\:\boldsymbol{{S}} \\ $$ Answered by JDamian last updated on 04/Feb/21 $${S}=\underset{{n}\geqslant\mathrm{1}}…
Question Number 131415 by mohammad17 last updated on 04/Feb/21 Commented by mohammad17 last updated on 04/Feb/21 $${can}\:{you}\:{help}\:{me} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 131412 by mohammad17 last updated on 04/Feb/21 Commented by mohammad17 last updated on 04/Feb/21 $${bow}\:{can}\:{solve}\:{this} \\ $$ Answered by physicstutes last updated on…
Question Number 65871 by behi83417@gmail.com last updated on 05/Aug/19 $$\mathrm{To}:\:\mathrm{sirAjfour},\mathrm{sir}:\mathrm{mrW1},\:\mathrm{sir}:\mathrm{MJS} \\ $$$$\mathrm{by}\:\mathrm{considering}\:\mathrm{my}\:\mathrm{comment}\:\mathrm{on}: \\ $$$$\mathrm{Q}#\mathrm{14535}\:\mathrm{and}\:\mathrm{sir}\:\mathrm{Ajfour}\:\mathrm{and}\:\mathrm{mrW1} \\ $$$$\mathrm{answer}'\mathrm{s}\:\mathrm{to}\:\mathrm{Q}#\mathrm{62839},\mathrm{I}\:\mathrm{think}\:\mathrm{now}\:\mathrm{we} \\ $$$$\mathrm{can}\:\mathrm{solve}\:\mathrm{Q}#\mathrm{14535}\:.\mathrm{if}\:\mathrm{you}\:\mathrm{have}\:\mathrm{time} \\ $$$$\mathrm{please}\:\mathrm{try}\:\mathrm{it}.\mathrm{I}\:\mathrm{know}\:\mathrm{there}\:\mathrm{is}\:\mathrm{a}\:\mathrm{relation} \\ $$$$\mathrm{between}\:\mathrm{this}\:\mathrm{questions}.\mathrm{but}\:\mathrm{can}'\mathrm{t}\:\mathrm{find}\:\mathrm{it}. \\ $$$$\mathrm{kindly}\:\mathrm{try}\:\mathrm{it}.\mathrm{thanks}\:\mathrm{alot}\:\mathrm{sir}. \\…
Question Number 65868 by aliesam last updated on 05/Aug/19 Commented by MJS last updated on 05/Aug/19 $$\mathrm{examine}\:\mathrm{the}\:\mathrm{function} \\ $$$${f}\left({x}\right)=\frac{\left(\mathrm{3}{x}−\mathrm{4}\right)\left(\mathrm{5}{x}+\mathrm{4}\right)}{\left(\mathrm{3}{x}−\mathrm{5}\right)\left({x}+\mathrm{5}\right)} \\ $$$$\mathrm{it}'\mathrm{s}\:\mathrm{defined}\:\mathrm{for}\:{x}\in\mathbb{R}\backslash\left\{−\mathrm{5};\:\frac{\mathrm{5}}{\mathrm{3}}\right\} \\ $$$$\mathrm{local}\:\mathrm{maximum}\:\mathrm{at}\:\begin{pmatrix}{\frac{\mathrm{109}−\sqrt{\mathrm{4921}}}{\mathrm{58}}}\\{\frac{\mathrm{383}−\mathrm{3}\sqrt{\mathrm{4921}}}{\mathrm{200}}}\end{pmatrix}\:\approx\begin{pmatrix}{.\mathrm{67}}\\{.\mathrm{86}}\end{pmatrix} \\ $$$$\mathrm{local}\:\mathrm{minimum}\:\mathrm{at}\:\begin{pmatrix}{\frac{\mathrm{109}+\sqrt{\mathrm{4921}}}{\mathrm{58}}}\\{\frac{\mathrm{383}+\mathrm{3}\sqrt{\mathrm{4921}}}{\mathrm{200}}}\end{pmatrix}\:\approx\begin{pmatrix}{\mathrm{3}.\mathrm{09}}\\{\mathrm{2}.\mathrm{97}}\end{pmatrix}…
Question Number 131391 by mohammad17 last updated on 04/Feb/21 Commented by mohammad17 last updated on 04/Feb/21 $${help}\:{me}\:{sir} \\ $$ Commented by mohammad17 last updated on…
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Question Number 131344 by Algoritm last updated on 03/Feb/21 Answered by bluberry508 last updated on 06/Feb/21 $$ \\ $$$$ \\ $$$$\left(\mathrm{1}+{i}\right)=\sqrt{\mathrm{2}}{e}^{\frac{{i}\pi}{\mathrm{4}}+\mathrm{2}{ai}\pi} \\ $$$$\left({a}\in\mathbb{Z}\right) \\ $$$$…