Question Number 104853 by ~blr237~ last updated on 24/Jul/20 $$\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:{Li}\left({x}^{\mathrm{2}} \right)−{Li}\left({x}\right)={ln}\mathrm{2} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 39156 by rahul 19 last updated on 03/Jul/18 Answered by MJS last updated on 03/Jul/18 $${f}\left({x}\right)={c}_{\mathrm{3}} {x}^{\mathrm{3}} +{c}_{\mathrm{2}} {x}^{\mathrm{2}} +{c}_{\mathrm{1}} {x}+{c}_{\mathrm{0}} \\ $$$${f}'\left({x}\right)=\mathrm{3}{c}_{\mathrm{3}}…
Question Number 39142 by rahul 19 last updated on 03/Jul/18 $$\mathrm{F}\left({x}\right)\:=\:{x}^{\mathrm{3}} −\mathrm{9}{x}^{\mathrm{2}} +\mathrm{24}{x}+{c}=\mathrm{0}\:{has}\:\mathrm{three} \\ $$$$\mathrm{real}\:\mathrm{and}\:\mathrm{distinct}\:\mathrm{roots}\:\alpha\:,\:\beta\:\&\:\gamma\:. \\ $$$$\mathrm{Q}.\mathrm{1}\:\rightarrow\:\mathrm{Possible}\:\mathrm{value}\:\mathrm{of}\:\mathrm{c}\:\mathrm{is}\:: \\ $$$$\mathrm{Q}.\mathrm{2}\:\rightarrow\:\mathrm{If}\:\left[\alpha\right]+\left[\beta\right]+\left[\gamma\right]=\:\mathrm{8}\:\mathrm{then}\:\mathrm{c}\:\mathrm{is}\:: \\ $$$$\mathrm{Q}.\mathrm{3}\:\rightarrow\:\mathrm{If}\:\left[\alpha\right]+\left[\beta\right]+\left[\gamma\right]=\mathrm{7}\:\mathrm{then}\:\mathrm{c}\:\mathrm{is}\:: \\ $$$$ \\ $$$$\mathrm{Options}\:\mathrm{for}\:\mathrm{the}\:\mathrm{above}\:\mathrm{3}\:\mathrm{Q}.\:\rightarrow…
Question Number 170155 by cortano1 last updated on 17/May/22 $$\:\:{Given}\:{f}\left({x}\right)={x}\sqrt{\mathrm{1}−{x}+\sqrt{\mathrm{1}−{x}}} \\ $$$$\:{where}\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1} \\ $$$$\:{find}\:{max}\:{f}\left({x}\right) \\ $$ Answered by Mathspace last updated on 18/May/22 $${x}\in\left[\mathrm{0},\mathrm{1}\right]\:\Rightarrow{x}={cos}\theta\:\Rightarrow \\…
Question Number 104608 by ~blr237~ last updated on 22/Jul/20 $$\:\:{D}^{\frac{\mathrm{1}}{\mathrm{2}}} \left({y}\right)=\mathrm{1}\:\:\:\:\:\Rightarrow\:\:\:{y}\left({x}\right)=\sqrt{\frac{{x}}{\pi}} \\ $$ Answered by OlafThorendsen last updated on 22/Jul/20 $${n}\in\mathbb{N},\:\nu\in\mathbb{C},\:\left({x}^{\nu} \right)^{\left({n}\right)} \:=\:\frac{\Gamma\left(\nu+\mathrm{1}\right)}{\Gamma\left(\nu+\mathrm{1}−{n}\right)}{x}^{\nu−{n}} \\ $$$$\mathrm{By}\:\mathrm{generalizing}\::…
Question Number 104604 by ~blr237~ last updated on 22/Jul/20 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+…+\frac{\mathrm{1}}{{n}}\right)\frac{\mathrm{1}}{\mathrm{2}^{{n}} }\:\:=\:{ln}\mathrm{4} \\ $$ Answered by OlafThorendsen last updated on 22/Jul/20 $$\mathrm{S}\:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+…+\frac{\mathrm{1}}{{n}}\right)\frac{\mathrm{1}}{\mathrm{2}^{{n}}…
Question Number 38905 by Raj Singh last updated on 01/Jul/18 Answered by MrW3 last updated on 01/Jul/18 $$\frac{{a}}{\mathrm{sin}\:{A}}=\frac{{b}}{\mathrm{sin}\:{B}}=\frac{{c}}{\mathrm{sin}\:{C}}={k}\:\left({constant}\right) \\ $$$${let}\:{dA}\:={little}\:{change}\:{in}\:{angle}\:{A} \\ $$$$ \\ $$$${B}=\mathrm{180}−{C}−{A} \\…
Question Number 104302 by bobhans last updated on 20/Jul/20 Commented by bobhans last updated on 21/Jul/20 $${by}\:{parts} \\ $$$$\begin{cases}{{u}=\mathrm{arc}\:\mathrm{tan}\:\left(\frac{\mathrm{1}}{\mathrm{2}{x}^{\mathrm{2}} }\right)\:\Rightarrow{du}\:=\frac{−\frac{\mathrm{1}}{{x}^{\mathrm{3}} }}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{4}{x}^{\mathrm{4}} }}\:{dx}}\\{{dv}\:=\:{dx}\:\Rightarrow{v}\:=\:{x}}\end{cases} \\ $$$${I}=\:{x}\:\mathrm{arc}\:\mathrm{tan}\:\left(\frac{\mathrm{1}}{\mathrm{2}{x}^{\mathrm{2}} }\right)+\int\:\frac{\mathrm{4}{x}^{\mathrm{2}}…
Question Number 38762 by Raj Singh last updated on 29/Jun/18 Commented by tanmay.chaudhury50@gmail.com last updated on 29/Jun/18 Commented by abdo.msup.com last updated on 29/Jun/18 $${we}\:{have}\:{f}\left({x}\right)={arctan}\left({cosx}\:+{sinx}\right)…
Question Number 169826 by cortano1 last updated on 10/May/22 $$\:\:{Given}\:{f}\left({x}\right)=\sqrt{\mathrm{sin}\:{x}}\:+\sqrt{\mathrm{3}\:\mathrm{cos}\:{x}}\: \\ $$$$\:\:{x}\in\:\left(\mathrm{0},\:\frac{\pi}{\mathrm{2}}\right) \\ $$$$\:{Find}\:{max}\:{f}\left({x}\right).\: \\ $$ Answered by mr W last updated on 10/May/22 $${f}'\left({x}\right)=\frac{\mathrm{cos}\:{x}}{\mathrm{2}\sqrt{\mathrm{sin}\:{x}}}−\frac{\mathrm{3sin}\:{x}}{\mathrm{2}\sqrt{\mathrm{3}\:\mathrm{cos}\:{x}}}=\mathrm{0}…