Question Number 222466 by klipto last updated on 27/Jun/25 $$\mathrm{find}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{term}.\: \\ $$ Commented by klipto last updated on 27/Jun/25 Commented by Frix last updated on…
Question Number 222424 by wewji12 last updated on 26/Jun/25 $$\int_{\mathrm{2}} ^{\:\infty} \:\:\:\:\frac{\mathrm{d}{z}}{\mathrm{ln}\left({z}\right)}−\underset{{l}=\mathrm{2}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{ln}\left({l}\right)}=?? \\ $$ Answered by MrGaster last updated on 26/Jun/25 $${I}=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\int_{{z}}…
Question Number 222425 by klipto last updated on 26/Jun/25 $$\boldsymbol{\mathrm{lim}}_{\boldsymbol{\mathrm{x}}\rightarrow\infty} \left(\mathrm{4}\boldsymbol{\mathrm{x}}+\sqrt{\mathrm{16}\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{3}\boldsymbol{\mathrm{x}}}\right) \\ $$$$\boldsymbol{\mathrm{ans}}:\frac{\mathrm{3}}{\mathrm{8}} \\ $$ Answered by Frix last updated on 26/Jun/25 $$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\left(\mathrm{4}{x}+\sqrt{\mathrm{16}{x}^{\mathrm{2}}…
Question Number 222427 by Nadirhashim last updated on 26/Jun/25 $$\:\:\boldsymbol{{if}}\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\boldsymbol{{sin}}\mathrm{2}\boldsymbol{{x}}}{\boldsymbol{{x}}^{\mathrm{3}} }+\frac{\boldsymbol{{a}}}{\boldsymbol{{x}}^{\mathrm{2}} }+\boldsymbol{{b}}\right)=\mathrm{1}\: \\ $$$$\:\:\:\:\boldsymbol{{find}}\:\boldsymbol{{a}}\:\boldsymbol{{and}}\:\boldsymbol{{b}}\:\:\boldsymbol{{without}} \\ $$$$\:\:\:\:\:\:\boldsymbol{{using}}\:\boldsymbol{{LH}}{opial}\:{rule} \\ $$ Answered by mr W last updated…
Question Number 222436 by ajfour last updated on 26/Jun/25 Commented by ajfour last updated on 26/Jun/25 https://youtu.be/xLaPcyoBv2w?si=4zzxA2kFBwZVUHdh Answered by mr W last updated on 27/Jun/25…
Question Number 222422 by MrGaster last updated on 26/Jun/25 $$\mathrm{Prove}:\int_{\mathrm{0}} ^{+\infty} \frac{{x}^{\mathrm{2}} \mathrm{lnsinh}{x}}{\mathrm{cosh}\:\mathrm{3}{x}}{dx}=\frac{\mathrm{1}}{\mathrm{9}}\pi^{\mathrm{2}} {G}−\frac{\mathrm{5}}{\mathrm{108}}\pi^{\mathrm{3}} \mathrm{ln}\:\mathrm{2} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 222432 by Shrodinger last updated on 26/Jun/25 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{xsinxcosx}}{{tan}^{\mathrm{2}} {x}+{cotan}^{\mathrm{2}} {x}}{dx} \\ $$ Answered by MathematicalUser2357 last updated on 28/Jun/25 $$\mathrm{0}.\mathrm{112076} \\…
Question Number 222418 by Jgrads last updated on 26/Jun/25 $$\mathrm{Prove}\:\mathrm{that}:\: \\ $$$$\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}}\:\left[\:\mathrm{ln}^{\mathrm{2}} \left(\mathrm{n}\right)−\mathrm{2}\underset{\:\mathrm{0}} {\int}^{\:\mathrm{n}} \frac{\mathrm{lnt}}{\:\sqrt{\mathrm{1}+\mathrm{t}^{\mathrm{2}} }}\:\mathrm{dt}\:\right]=\:\frac{\pi^{\mathrm{2}} }{\mathrm{6}}+\mathrm{ln}^{\mathrm{2}} \left(\mathrm{2}\right) \\ $$ Answered by MrGaster last…
Question Number 222419 by ajfour last updated on 26/Jun/25 Commented by ajfour last updated on 26/Jun/25 $$\bar {{v}}=\mathrm{5}\left(\mathrm{sin}\:\theta\hat {{i}}+\mathrm{cos}\:\theta\hat {{j}}\right)\:\:\:\:\:\theta\:{constant}. \\ $$$${Find}\:\:\:\:\:\frac{{Y}}{{T}}\left(\theta\right).\:{Hence}\:\theta\:{such}\:{that} \\ $$$$\frac{{Y}}{{T}}\left(\theta\right)\:{is}\:{a}\:{maximum}. \\…
Question Number 222389 by MrGaster last updated on 25/Jun/25 $$\mathrm{Prove}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{cos}\left({nx}\right)\mathrm{cos}\left({p}\:\mathrm{arctan}\:{x}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\frac{{p}}{\mathrm{2}}} }=\frac{\pi}{\mathrm{2}}\:\frac{{n}^{{p}−\mathrm{1}} {e}^{−{n}} }{\Gamma\left({p}\right)}\:\left({p}>\mathrm{0}\right) \\ $$ Terms of Service Privacy Policy…