Question Number 74799 by mathmax by abdo last updated on 30/Nov/19 $${prove}\:{that}\:\mathrm{0}\leqslant\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{t}^{\mathrm{2}} \:{e}^{−{nt}} }{{e}^{{t}} −\mathrm{1}}{dt}\:\leqslant\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\:\:{for}\:{n}\:{integr}\:{not}\:\mathrm{0} \\ $$ Answered by mind is power…
Question Number 74796 by mathmax by abdo last updated on 30/Nov/19 $${let}\:{U}_{{n}} =\left(−\mathrm{1}\right)^{{n}} \left\{{arcsin}\left(\frac{\mathrm{1}}{{n}}\right)−\frac{\mathrm{1}}{{n}}\right\}^{\frac{\mathrm{1}}{\mathrm{3}}} \\ $$$${study}\:{the}\:{convergence}\:{of}\:\Sigma\:{U}_{{n}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 140334 by mnjuly1970 last updated on 06/May/21 $$ \\ $$$$\:\:\:\:\:{calculate}\::: \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{\xi}\::=\:\int_{−\infty} ^{\:\infty} {ln}\left(\mathrm{2}−\mathrm{2}{cos}\left({x}^{\mathrm{2}} \right)\right){dx}=? \\ $$$$ \\ $$ Answered by ArielVyny last…
Question Number 74797 by mathmax by abdo last updated on 30/Nov/19 $${find}\:{nsture}\:{of}\:{the}\:{serie}\:\Sigma\:{sin}\left(\pi{en}!\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 140329 by benjo_mathlover last updated on 06/May/21 $$\:\mathrm{x}^{\lfloor\mathrm{x}\rfloor} \:+\:\mathrm{x}^{\lceil\mathrm{x}\rceil} \:=\:\frac{\mathrm{175}}{\mathrm{8}} \\ $$ Answered by john_santu last updated on 06/May/21 $$\:\mathrm{0}<{x}<\mathrm{1}\rightarrow\:{x}^{\mathrm{0}} \:+\:{x}^{\mathrm{1}} \:=\:\frac{\mathrm{175}}{\mathrm{8}} \\…
Question Number 74794 by mathmax by abdo last updated on 30/Nov/19 $${let}\:{A}\:=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\:\:\:\mathrm{2}}\\{−\mathrm{1}\:\:\:\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}^{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:{e}^{{A}} \:{and}\:{e}^{−{A}} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\:{cosA}\:{and}\:{sinA} \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\:{ch}\left({A}\right)\:{and}\:{sh}\left({A}\right) \\ $$ Commented by…
Question Number 74795 by mathmax by abdo last updated on 30/Nov/19 $${study}\:{the}\:{convergence}\:{of}\:\Sigma\:\frac{\mathrm{1}}{{nH}_{{n}} } \\ $$$${with}\:{H}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}} \\ $$ Commented by mathmax by abdo…
Question Number 140330 by Satyendra last updated on 06/May/21 $${Find}\:{the}\:{Integration}\:{Value}: \\ $$$$\mathrm{1} \:\int\frac{\sqrt{{x}}{d}\left({x}\right)}{\mathrm{1}+^{\mathrm{3}} \sqrt{{x}}}=? \\ $$$$\mathrm{2} \int\frac{{dx}}{{x}^{\frac{\mathrm{1}}{\mathrm{2}}} −{x}^{\frac{\mathrm{1}}{\mathrm{4}}} }=? \\ $$ Answered by john_santu last…
Question Number 74793 by mathmax by abdo last updated on 30/Nov/19 $${prove}\:{the}\:{convergence}\:{of}\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+\sqrt{{x}}\right)}{\:\sqrt{{x}}}{dx} \\ $$ Commented by mathmax by abdo last updated on 06/Dec/19…
Question Number 140325 by liberty last updated on 06/May/21 $$ \\ $$What is the equation of the circle, if the circle is tangential to the…