Question Number 221081 by SdC355 last updated on 24/May/25 $$\mathrm{for}\:\mathrm{all}\:{m},{n},{p}\in\mathbb{R} \\ $$$$\left(\mathrm{g}\left({m}\right)+{n}\right)\left(\mathrm{g}\left({n}\right)+{m}\right)={p}^{\mathrm{2}} \left(\mathrm{perfect}\:\mathrm{square}\:\mathrm{number}\right) \\ $$$$\mathrm{find}\:\mathrm{function}\:\mathrm{g};\mathbb{N}\rightarrow\mathbb{N} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 221078 by MrGaster last updated on 24/May/25
Question Number 221095 by SdC355 last updated on 24/May/25 $$\mathrm{Complex}\:\mathrm{integral} \\ $$$$\mathrm{1}.\:\int_{−\infty} ^{\:+\infty} \:\:\:\frac{\mathrm{d}{z}}{\left({z}^{\mathrm{2}} +\mathrm{1}\right)^{\nu} }=?? \\ $$$$\mathrm{2}.\:\int_{−\infty} ^{+\infty} \:\:\frac{{e}^{\boldsymbol{{i}}\pi{t}} }{{t}^{\mathrm{2}} +\mathrm{1}}\:\mathrm{d}{t}=?? \\ $$$$\mathrm{3}.\:\oint_{\:{C}} \:\frac{\mathrm{1}}{{z}}\:\mathrm{d}{z}=??\:,\:{C};{x}^{\mathrm{2}}…
Question Number 221036 by SdC355 last updated on 23/May/25 $$\mathrm{prove} \\ $$$$\int_{{P}\in\left[\epsilon,\epsilon+\delta\right]} \sqrt{\left(\frac{\mathrm{d}\:\:}{\mathrm{d}{t}}{f}\left({t}\right)\right)^{\mathrm{2}} +\left(\frac{\mathrm{d}\:\:}{\mathrm{d}{t}}\mathrm{g}\left({t}\right)\right)^{\mathrm{2}} }\:\mathrm{d}{t}\leq\int_{{P}\in\left[\epsilon,\epsilon+\delta\right]} \:\frac{{C}_{\mathrm{1}} {f}^{\left(\mathrm{1}\right)} \left({t}\right)+{C}_{\mathrm{2}} \mathrm{g}^{\left(\mathrm{1}\right)} \left({t}\right)}{\:\sqrt{{C}_{\mathrm{1}} ^{\mathrm{2}} +{C}_{\mathrm{2}} ^{\mathrm{2}} }}\:\mathrm{d}{t} \\…
Question Number 220976 by SdC355 last updated on 21/May/25 $$\int_{−\infty} ^{\:+\infty} \int_{−\infty} ^{\:+\infty} \:{e}^{−\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)} \mathrm{d}{V}\:\rightarrow\int_{\mathrm{0}} ^{\:\mathrm{2}\pi} \int_{\mathrm{0}} ^{\:\infty} \:{r}\centerdot{e}^{−{r}^{\mathrm{2}} } \mathrm{d}{r}\mathrm{d}\theta=\pi \\ $$$$\mathrm{i}\:\mathrm{can}'\mathrm{t}\:\mathrm{understand}\:\mathrm{domain}\:\mathrm{of}\:\mathrm{integration}…
Question Number 220972 by SdC355 last updated on 21/May/25 $$\int_{−\infty} ^{+\infty} \int_{−\infty} ^{+\infty} \:\:\:\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{4}\right)^{\mathrm{2}} }\:\mathrm{d}{x}\mathrm{d}{y} \\ $$$${x}={r}\mathrm{cos}\left(\theta\right) \\ $$$${y}={r}\mathrm{sin}\left(\theta\right) \\ $$$$\mid\mid\boldsymbol{{J}}\mid\mid={r}\mathrm{d}{r}\mathrm{d}\theta \\ $$$$\int_{\mathrm{0}}…
Question Number 220973 by MrGaster last updated on 21/May/25 $$\mathrm{Prove}:\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\left(−\frac{\mathrm{1}}{\mathrm{3}}\right)^{{k}} \mathrm{cos}^{\mathrm{3}} \left(\mathrm{3}^{{k}−{n}} \pi\right)=\frac{\mathrm{3}}{\mathrm{4}}\left[\left(−\frac{\mathrm{1}}{\mathrm{3}}\right)^{{n}+\mathrm{1}} +\mathrm{cos}\frac{\pi}{\mathrm{3}^{{n}} }\right] \\ $$ Answered by universe last updated on…
Question Number 220913 by SdC355 last updated on 20/May/25 $$\mathrm{Is}\:\mathrm{there}\:\mathrm{an}\:\mathrm{Manager}??? \\ $$$$\mathrm{pls}\:\mathrm{ban}\:\mathrm{Question}\:\mathrm{Spamming}\:\mathrm{and}… \\ $$$$\mathrm{pls}\:\mathrm{fix}\:\mathrm{invisible}\:\mathrm{line}\:\mathrm{matrix}\:\mathrm{bug} \\ $$ Commented by mr W last updated on 21/May/25 $${the}\:{developer}\:{Tinku}\:{Tara}\:{doesn}'{t}…
Question Number 220820 by SdC355 last updated on 19/May/25 Commented by SdC355 last updated on 19/May/25 $$\mathrm{Q220800} \\ $$ Answered by MathematicalUser2357 last updated on…
Question Number 220790 by SdC355 last updated on 19/May/25 $$\mathrm{Complex}\:\mathrm{integral} \\ $$$$\oint_{\:\mathrm{C}} \:\frac{\mathrm{d}{z}}{{z}^{\mathrm{3}} +\mathrm{1}}=??\:,\:{C};{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{4} \\ $$$$\oint_{\:{C}} \:\frac{\mathrm{1}}{{z}}{e}^{{z}} \:\mathrm{d}{z},\:{C};\begin{cases}{{y}=\mathrm{1}\:,\:−\mathrm{1}\leq{x}\leq\mathrm{1}}\\{{y}=−\mathrm{1}\:,\:−\mathrm{1}\leq{x}\leq\mathrm{1}}\\{{x}=\mathrm{1}\:,\:−\mathrm{1}\leq{y}\leq\mathrm{1}}\\{{x}=−\mathrm{1}\:,\:−\mathrm{1}\leq{y}\leq\mathrm{1}}\end{cases}\: \\ $$ Answered by vnm…