Question Number 134064 by mr W last updated on 27/Feb/21 Commented by mr W last updated on 27/Feb/21 $${find}\:{the}\:{angle}\:\theta\:{at}\:{which}\:{the}\:{falling} \\ $$$${rod}\:{begins}\:{to}\:{slip}\:{on}\:{the}\:{ground}\:{if} \\ $$$${the}\:{friction}\:{coefficient}\:{between}\:{rod} \\ $$$${and}\:{ground}\:{is}\:\mu.…
Question Number 134067 by bramlexs22 last updated on 27/Feb/21 $$\:\mathrm{Calculate}\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\underset{\mathrm{k}=\mathrm{2}} {\overset{\mathrm{n}} {\prod}}\:\frac{\mathrm{k}^{\mathrm{3}} −\mathrm{1}}{\mathrm{k}^{\mathrm{3}} +\mathrm{1}}\:=\:? \\ $$ Answered by john_santu last updated on 27/Feb/21 $$\:{since}\:\frac{{k}^{\mathrm{3}}…
Question Number 68528 by Joel122 last updated on 13/Sep/19 $$\underset{{t}\rightarrow\infty} {\mathrm{lim}}\:\left[\frac{\mathrm{1}}{{t}}\:\int_{\mathrm{1}} ^{\:{t}} \:\sqrt[{{x}}]{{t}}\:{dx}\right] \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 134061 by benjo_mathlover last updated on 27/Feb/21 $$\mathrm{If}\:\Sigma\:\mathrm{a}_{\mathrm{n}} \:\mathrm{is}\:\mathrm{a}\:\mathrm{convergent}\:\mathrm{series}\:\mathrm{of} \\ $$$$\mathrm{nonnegative}\:\mathrm{terms},\mathrm{what}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{said}\:\mathrm{about}\:\Sigma\:\mathrm{a}_{\mathrm{n}} .\mathrm{a}_{\mathrm{n}+\mathrm{1}} \:? \\ $$$$\left(\mathrm{a}\right)\:\mathrm{always}\:\mathrm{converges} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{always}\:\mathrm{diverges} \\ $$$$\left(\mathrm{c}\right)\:\mathrm{may}\:\mathrm{converges}\:\mathrm{or}\:\mathrm{diverge} \\ $$…
Question Number 134060 by benjo_mathlover last updated on 27/Feb/21 $$\mathrm{If}\:\mathrm{p}>\mathrm{1}\:\mathrm{and}\:\mathrm{q}>\mathrm{1}\:\mathrm{what}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{said}\:\mathrm{about}\:\mathrm{the}\:\mathrm{convergence}\: \\ $$$$\mathrm{of}\:\underset{\mathrm{n}=\mathrm{2}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{p}} .\left(\mathrm{ln}\:\mathrm{n}\right)^{\mathrm{q}} }\:? \\ $$$$\left(\mathrm{a}\right)\:\mathrm{always}\:\mathrm{converges} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{always}\:\mathrm{diverges} \\ $$$$\left(\mathrm{c}\right)\:\mathrm{may}\:\mathrm{converges}\:\mathrm{or}\:\mathrm{diverges} \\…
Question Number 68524 by Maclaurin Stickker last updated on 13/Sep/19 Answered by mr W last updated on 13/Sep/19 Commented by Maclaurin Stickker last updated on…
Question Number 134062 by BHOOPENDRA last updated on 27/Feb/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 134058 by john_santu last updated on 27/Feb/21 $$\mathcal{J}\:=\:\int\:\frac{{dx}}{\mathrm{1}+\mathrm{tan}\:{x}+\mathrm{csc}\:{x}+\mathrm{cot}\:{x}+\mathrm{sec}\:{x}} \\ $$ Answered by john_santu last updated on 27/Feb/21 $$\mathcal{J}=\int\:\frac{{dx}}{\mathrm{1}+\frac{\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}+\frac{\mathrm{1}}{\mathrm{sin}\:{x}}+\frac{\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}}+\frac{\mathrm{1}}{\mathrm{cos}\:{x}}} \\ $$$$\:=\:\int\:\frac{\mathrm{cos}\:{x}\:\mathrm{sin}\:{x}}{\mathrm{sin}\:{x}\mathrm{cos}\:{x}+\mathrm{sin}\:^{\mathrm{2}} {x}+\mathrm{cos}\:^{\mathrm{2}} {x}+\mathrm{sin}\:{x}} \\…
Question Number 68521 by naka3546 last updated on 13/Sep/19 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{4}\:\mathrm{sin}\:{x}\:+\:\mathrm{2}\:\mathrm{tan}\:{x}\:−\:\mathrm{6}{x}}{{x}^{\mathrm{5}} }\:\:=\:\:? \\ $$$${Without}\:\:{L}'{Hospital} \\ $$ Commented by mathmax by abdo last updated on 13/Sep/19…
Question Number 2983 by Syaka last updated on 02/Dec/15 $$\underset{\mathrm{2}} {\overset{{m}} {\int}}\:{f}\left({x}\right)\:{dx}\:=\:\underset{{n}\:\rightarrow\:\infty} {{lim}}\:\underset{{k}\:=\:\mathrm{1}} {\overset{{n}} {\sum}}\:\left(\mathrm{1}\:+\frac{{k}}{{n}}\right)\left(\frac{\mathrm{2}{k}}{{n}}\right) \\ $$$$ \\ $$$${m}\:+\:{f}\left({m}\right)\:=\:? \\ $$ Commented by prakash jain…