Question Number 104856 by ~blr237~ last updated on 24/Jul/20 $$\underset{{z}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\overset{−} {{z}}}{{z}}\:\:\:\:,\:\:\:\:\underset{{z}\rightarrow{i}} {\mathrm{lim}}\:\frac{\left(\overset{−} {{z}}\right)^{\mathrm{4}} }{{z}^{\mathrm{4}} }\:\:,\underset{{z}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{sinz}}{{z}}\: \\ $$ Answered by abdomathmax last updated on…
Question Number 104858 by ~blr237~ last updated on 24/Jul/20 $$\:\:\left(\mathrm{1}−{a}^{\mathrm{3}} \right)\left(\mathrm{1}−{b}^{\mathrm{3}} \right)……\left(\mathrm{1}−{x}^{\mathrm{3}} \right)\left(\mathrm{1}−{y}^{\mathrm{3}} \right)\left(\mathrm{1}−{z}^{\mathrm{3}} \right)\:\:\:\:\:\:\:\:???? \\ $$ Commented by 1549442205PVT last updated on 24/Jul/20 $$\boldsymbol{\mathrm{what}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{your}}\:\:\boldsymbol{\mathrm{question}}?…
Question Number 104857 by ~blr237~ last updated on 24/Jul/20 $$\:\:{y}'=\frac{{y}−{x}}{{y}+{x}}\:\:\:\:\:\:\:{y}\left(\mathrm{0}\right)=\mathrm{0} \\ $$ Answered by bemath last updated on 24/Jul/20 $${y}={px}\:\Rightarrow\:\frac{{dy}}{{dx}}\:=\:{p}+{x}\frac{{dp}}{{dx}} \\ $$$$\Leftrightarrow{p}+{x}\frac{{dp}}{{dx}}\:=\:\frac{{x}\left({p}−\mathrm{1}\right)}{{x}\left({p}+\mathrm{1}\right)} \\ $$$${x}\frac{{dp}}{{dx}}\:=\:\frac{{p}−\mathrm{1}}{{p}+\mathrm{1}}−\frac{{p}\left({p}+\mathrm{1}\right)}{{p}+\mathrm{1}} \\…
Question Number 104852 by ~blr237~ last updated on 24/Jul/20 $$\:\:{if}\:\:{g}\in{C}\left(\mathbb{R},\mathbb{R}\right)\:{and}.\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{g}\left({x}\right){dx}=\frac{\mathrm{1}}{\mathrm{3}}+\int_{\mathrm{0}} ^{\mathrm{1}} {g}^{\mathrm{2}} \left({x}^{\mathrm{2}} \right){dx}\: \\ $$$${then}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} {g}\left({x}\right){dx}=\frac{\mathrm{2}}{\mathrm{3}}\:{and}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} {g}^{\mathrm{2}} \left({x}\right){dx}=\frac{\mathrm{1}}{\mathrm{2}}\:\: \\ $$…
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}}…