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…
Question Number 134052 by shaker last updated on 27/Feb/21 Answered by mathmax by abdo last updated on 27/Feb/21 $$\mathrm{I}\:=\int\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{x}^{\mathrm{6}} \:+\mathrm{3}}\mathrm{dx}\:\:\Rightarrow\mathrm{I}\:=\int\:\:\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{x}^{\mathrm{6}} \:+\left(\mathrm{3}^{\frac{\mathrm{1}}{\mathrm{6}}} \right)^{\mathrm{6}} }\mathrm{dx}\:=_{\mathrm{x}=\mathrm{3}^{\frac{\mathrm{1}}{\mathrm{6}}}…
Question Number 68517 by A8;15: last updated on 12/Sep/19 Terms of Service Privacy Policy Contact: info@tinkutara.com