Question Number 222261 by MathematicalUser2357 last updated on 21/Jun/25 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{tan}\left({x}^{\mathrm{2}} +\mathrm{4}{x}\right)}{\mathrm{sin}\left(\mathrm{9}{x}^{\mathrm{2}} +{x}\right)} \\ $$$$\mathrm{No}\:\mathrm{L}'\mathrm{h}\hat {\mathrm{o}pital}'\mathrm{s}\:\mathrm{rule}\:\mathrm{allowed}! \\ $$ Answered by gregori last updated on 21/Jun/25…
Question Number 222288 by hardmath last updated on 21/Jun/25 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{1}\:+\:\mathrm{2}\:+\:\mathrm{3}\:+\:…\:+\:\boldsymbol{\mathrm{n}}\:=\:\frac{\mathrm{n}\centerdot\left(\mathrm{n}\:+\:\mathrm{1}\right)}{\mathrm{2}} \\ $$ Answered by A5T last updated on 21/Jun/25 $$\mathrm{1}+\mathrm{2}+\mathrm{3}+…+\mathrm{n}−\mathrm{2}+\mathrm{n}−\mathrm{1}+\mathrm{n}\:=\mathrm{x} \\ $$$$\mathrm{n}+\mathrm{n}−\mathrm{1}+\mathrm{n}−\mathrm{2}+…+\mathrm{3}+\mathrm{2}+\mathrm{1}=\mathrm{x} \\…
Question Number 222284 by klipto last updated on 21/Jun/25 $$\boldsymbol{\mathrm{y}}=\frac{\mathrm{8}^{\boldsymbol{\mathrm{x}}} }{\left(\boldsymbol{\mathrm{in}}\mathrm{8}\right)^{\mathrm{3}} } \\ $$$$\boldsymbol{\mathrm{find}}\:\frac{\boldsymbol{\mathrm{d}}^{\mathrm{6}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{6}} } \\ $$ Answered by mr W last updated on…
Question Number 222285 by Shrodinger last updated on 21/Jun/25 $$\int\frac{{x}^{\mathrm{5}} −{x}^{\mathrm{3}} +\mathrm{2}{x}+\mathrm{1}}{{x}^{\mathrm{4}} +\mathrm{1}}\:{e}^{−\frac{\mathrm{1}}{\mathrm{4}}{ln}\left({x}^{\mathrm{4}} +\mathrm{1}\right)} {dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 222280 by klipto last updated on 21/Jun/25 $$\boldsymbol{\mathrm{y}}=\mathrm{3}\boldsymbol{\mathrm{x}}^{\mathrm{2024}} −\mathrm{18}\boldsymbol{\mathrm{x}}^{\mathrm{2020}} +\mathrm{5}\boldsymbol{\mathrm{x}}^{\mathrm{47}} −\mathrm{8} \\ $$$$\boldsymbol{\mathrm{find}}\:\frac{\boldsymbol{\mathrm{d}}^{\mathrm{2025}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{2025}} } \\ $$ Commented by mr W last updated…
Question Number 222249 by MrGaster last updated on 21/Jun/25 $$\mathrm{Prove}:\forall{n}\in\mathbb{Z}^{+} ,\mathrm{1}^{\mathrm{3}} +\mathrm{2}^{\mathrm{3}} +\ldots+{n}^{\mathrm{3}} =\left(\mathrm{1}+\mathrm{2}+\ldots+{n}\right)^{\mathrm{2}} \\ $$ Answered by MrGaster last updated on 21/Jun/25 Answered by…
Question Number 222276 by Nicholas666 last updated on 27/Jun/25 $$ \\ $$$$\:\mathrm{Prove};\:\underset{{k}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{k}}{\mathrm{sinh}\left(\pi{k}\right)}\:=\:\frac{\Gamma\left(\frac{\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{4}} −\:\mathrm{8}\pi^{\mathrm{2}} }{\mathrm{32}\pi^{\mathrm{3}} }\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$ Terms of Service Privacy…
Question Number 222279 by fantastic last updated on 21/Jun/25 $$\left({a}^{\mathrm{2}} −{b}^{\mathrm{2}} \right)\mathrm{sin}\:\theta+\mathrm{2}{ab}\mathrm{cos}\:\theta={a}^{\mathrm{2}} +{b}^{\mathrm{2}} \\ $$$$\mathrm{tan}\:\theta=?? \\ $$ Answered by mr W last updated on 21/Jun/25…
Question Number 222275 by Nicholas666 last updated on 21/Jun/25 $$ \\ $$$$\:\:\mathrm{Prove}\:;\:\int_{−\pi} ^{\:\pi} \:\frac{{z}\:\mathrm{sin}\left({z}\right)\:}{\left(\mathrm{1}\:+\:{z}\:+\:\sqrt{\mathrm{1}\:+\:{z}^{\mathrm{2}} }\right)\sqrt{\mathrm{3}\:+\:\mathrm{sin}^{\mathrm{2}} \left({z}\right)}}\:{dz}\:=\:\zeta\left(\mathrm{2}\right)\:\:\:\:\:\:\:\: \\ $$$$ \\ $$ Answered by MrGaster last updated…
Question Number 222197 by BHOOPENDRA last updated on 20/Jun/25 $${question}\:\mathrm{211277} \\ $$ Answered by BHOOPENDRA last updated on 20/Jun/25 Commented by BHOOPENDRA last updated on…