[Step-by-Step] Show that a formula for the curvature of any plane curve α(t)=(x(t), y(t)) is given by \kappa_alpha=(|x^prime y^prime \prime-x^prime
Question: Show that a formula for the curvature of any plane curve \(\alpha(t)=(x(t), y(t))\) is given by
\[\kappa_{\alpha}=\frac{\left|x^{\prime} y^{\prime \prime}-x^{\prime \prime} y^{\prime}\right|}{\left(x^{\prime 2}+y^{\prime 2}\right)^{3 / 2}}\]
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![[Solution Library] Show that, for any helix,](/images/solutions/MC-solution-library-73503.jpg "[Solution Library] Show that, for any helix, the Darboux vector")
[Solution Library] Show that, for any helix, the Darboux vector
(Solution Library) Find a curve σ(s) with \kappa_σ(s)=(1)/(1+s^2)
![[Solution] Let σ be a closed curve](/images/solutions/MC-solution-library-73505.jpg "[Solution] Let σ be a closed curve enclosing a region R.")
[Solution] Let σ be a closed curve enclosing a region R.
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[Step-by-Step] For the paraboloid z=x^2+y^2 define a non-Monge
(Solution Library) Homework: What are the parameter curves for
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