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Question-226467

Question Number 226467 by Lara2440 last updated on 30/Nov/25 Answered by Lara2440 last updated on 30/Nov/25 $$\:\mathrm{let}\:\mathrm{differantable}\:\mathrm{Smooth}\:\mathrm{curve}\:\phi;\mathbb{R}^{\mathrm{2}} \rightarrow\mathbb{R}^{\mathrm{3}} \\ $$$$\:\phi\left({u},{v}\right)=\begin{cases}{−\mathrm{sin}\left({u}\right)−\mathrm{3sin}\left({v}\right)}\\{\mathrm{cos}\left({u}\right)+\mathrm{3cos}\left({v}\right)}\\{\mathrm{4}{v}}\end{cases}\:\:\:,\:−\mathrm{2}\pi\leq{u}\leq\mathrm{2}\pi\:,\:−\mathrm{2}\pi\leq{v}\leq\mathrm{2}\pi \\ $$$$\mathrm{Find}\:\mathrm{Normal}\:\mathrm{curvature}\:,\:\mathrm{Principal}\:\mathrm{curvature}\:,\:\mathrm{Principal}\:\mathrm{dirction} \\ $$$$\: \\…

Question-226455

Question Number 226455 by Spillover last updated on 29/Nov/25 Answered by Ghisom_ last updated on 29/Nov/25 $$\frac{\mathrm{2}−{x}^{\mathrm{2}} }{\left(\mathrm{1}−{x}\right)\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}=\frac{\mathrm{1}+\mathrm{1}−{x}^{\mathrm{2}} }{\left(\mathrm{1}−{x}\right)\sqrt{\left(\mathrm{1}−{x}\right)\left(\mathrm{1}+{x}\right)}}= \\ $$$$=\frac{\mathrm{1}}{\left(\mathrm{1}−{x}\right)^{\mathrm{3}/\mathrm{2}} \left(\mathrm{1}+{x}\right)^{\mathrm{1}/\mathrm{2}} }+\frac{\left(\mathrm{1}−{x}\right)\left(\mathrm{1}+{x}\right)}{\left(\mathrm{1}−{x}\right)^{\mathrm{3}/\mathrm{2}} \left(\mathrm{1}+{x}\right)^{\mathrm{1}/\mathrm{2}}…

Question-226464

Question Number 226464 by Spillover last updated on 29/Nov/25 Commented by Frix last updated on 29/Nov/25 $$\mathrm{By}\:\mathrm{parts} \\ $$$${u}'=\mathrm{1}\:\rightarrow\:{u}={x} \\ $$$${v}=\mathrm{cot}^{−\mathrm{1}} \:\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)\:\rightarrow\:{v}'=−\frac{\mathrm{2}{x}−\mathrm{1}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{2}\right)}…

Question-226442

Question Number 226442 by mr W last updated on 28/Nov/25 Commented by mahdipoor last updated on 29/Nov/25 $$\mathrm{for}\:\mathrm{mass}\:\mathrm{M} \\ $$$$\Sigma\mathrm{F}=\mathrm{ma}\:\:\left(\mathrm{for}\:\mathrm{CM}\right) \\ $$$$\begin{cases}{\mathrm{A}=\left(\overset{..} {\mathrm{x}}−\alpha.\mathrm{l}.\mathrm{cos}\theta−\omega^{\mathrm{2}} .\mathrm{l}.\mathrm{sin}\theta\right)\mathrm{M}}\\{\mathrm{B}=\left(−\alpha.\mathrm{l}.\mathrm{sin}\theta+\omega^{\mathrm{2}} .\mathrm{l}.\mathrm{cos}\theta\right)\mathrm{M}}\end{cases}…

Prove-klein-bottle-is-Immersion-but-klein-bottle-can-t-Imbedding-in-R-3-Space-

Question Number 226400 by Lara2440 last updated on 27/Nov/25 $$\mathrm{Prove}\:\mathrm{klein}\:\mathrm{bottle}\:\mathrm{is}\:\mathrm{Immersion} \\ $$$$\mathrm{but}\:\mathrm{klein}\:\mathrm{bottle}\:\mathrm{can}'\mathrm{t}\:\mathrm{Imbedding}\:\mathrm{in}\:\mathbb{R}^{\mathrm{3}} \:\mathrm{Space}\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com