Question Number 222487 by MathematicalUser2357 last updated on 28/Jun/25 $$'{Delete}\:{all}\:{lines}'\:{function}\:{deletes}\:{all}\:{lines}\:{without}\:{asking}\:{after}\:{deleting}\:{all}\:{lines}\:{for}\:{the}\:{first}\:{time}\:{in}\:{the}\:{equation}\:{editor} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 222462 by fantastic last updated on 27/Jun/25 $${i}^{{i}} =?? \\ $$ Answered by vnm last updated on 27/Jun/25 $$=\left({e}^{{i}\left(\frac{\pi}{\mathrm{2}}+\mathrm{2}{n}\pi\right)} \right)^{{i}} ={e}^{\pi\left(−\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{2}{n}\right)} ,\:{n}\in\mathbb{Z} \\…
Question Number 222441 by fantastic last updated on 27/Jun/25 $$\mathrm{0}^{{i}} \\ $$ Answered by wewji12 last updated on 27/Jun/25 $$\mathrm{0}\:\mathrm{because}\:{f}\left({z}\right)=\mathrm{0}^{{z}} \:\mathrm{for}\:\mathrm{all}\:{z}\in\mathbb{R}\backslash\left\{\mathrm{0}\right\} \\ $$$${f}\left({z}\right)=\mathrm{0}\:\mathrm{const}. \\ $$$${f}\left({z}\right)=\begin{cases}{\:\mathrm{1}\:,\:{z}=\mathrm{0}}\\{\:\mathrm{0}\:,\:{z}\in\mathbb{R}\backslash\left\{\mathrm{0}\right\}}\end{cases}…
Question Number 222466 by klipto last updated on 27/Jun/25 $$\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 $$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\left(\mathrm{4}{x}+\sqrt{\mathrm{16}{x}^{\mathrm{2}}…
Question Number 222365 by wewji12 last updated on 23/Jun/25 $$\mathrm{Prove} \\ $$$$\oint_{\:\partial\mathcal{S}} \:\overset{\rightarrow} {\boldsymbol{\mathrm{E}}}\centerdot\mathrm{d}\overset{\rightarrow} {\mathcal{S}}=\frac{\rho_{\mathrm{enc}} }{\boldsymbol{\varepsilon}_{\mathrm{0}} } \\ $$$$\overset{\rightarrow} {\boldsymbol{\mathrm{E}}}=\frac{\overset{\rightarrow} {\boldsymbol{\mathrm{r}}}}{\boldsymbol{\mathrm{r}}^{\mathrm{3}} }\: \\ $$ Answered…
Question Number 222356 by wewji12 last updated on 23/Jun/25 $$\int_{\mathrm{0}} ^{\:\infty} \:{f}\left({r}\right)\mathrm{d}{r}=\mathrm{1}\:,\:\int_{\mathrm{0}} ^{\:\infty} \:\mathrm{g}\left({r}\right)\mathrm{d}{r}=\mathrm{1} \\ $$$$\int_{−\infty\boldsymbol{{i}}+\boldsymbol{\gamma}} ^{\:\:\infty\boldsymbol{{i}}+\boldsymbol{\gamma}} \:{F}\left({t}\right){G}\left({t}\right)\mathrm{d}{t}=?? \\ $$$${F}\left({t}\right)=\int_{\mathrm{0}} ^{\:\infty} \:{f}\left({r}\right){e}^{−{rt}} \mathrm{d}{r}\:,\:{G}\left({t}\right)=\int_{\mathrm{0}} ^{\:\infty} \:\mathrm{g}\left({r}\right){e}^{−{rt}}…
Question Number 222300 by fantastic last updated on 22/Jun/25 $${How}\:{do}\:{you}\:{put}\:{a}\:{box}\:{around}\:{something}??\:{please}\:{tell}\:{me} \\ $$ Commented by mr W last updated on 22/Jun/25 $$\begin{array}{|c|}{{something}\:{like}\:{this}?}\\\hline\end{array} \\ $$ Commented by…
Question Number 222317 by wewji12 last updated on 22/Jun/25 $$\int_{\mathrm{0}} ^{\:\infty} \:{f}\left({z}\right)\mathrm{d}{z}=\frac{\pi}{\mathrm{2}}\:,\:\int_{\mathrm{0}} ^{\:\infty} \:\mathrm{g}\left({z}\right)\mathrm{d}{z}=\mathrm{1} \\ $$$$\frac{\mathrm{2}}{\pi}\int_{\mathrm{0}} ^{\:\infty} \:{f}\left({z}\right)\mathrm{g}\left({z}\right)\mathrm{d}{z}=?? \\ $$ Answered by MrGaster last updated…