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I am taking Calc III, but I am having a hard time understanding some of the concepts. Right now I am struggling with understanding the curvature of a line. What I have in my notes is this:

Curvature

second derivative (rate of change of tangent line)(rate of change w/ respect to arc length)

r = a smooth parameterized curve, s = arc length and T = the unit tangent vector = r'/Ir'I

curvature is κ(s) = dT/ds

then the professor got us from dT/ds to [dT/dt * 1/r'(t)] using the chain rule

so κ(s) = [dT/dt * 1/r'(t)]

Then the next class my notes have something regarding k = I a cross V I / I V I^{3}

I am assuming that this was in regards to acceleration and velocity

I understand that curvature is the rate of change of the tangent line, but I don't know how I would approach a problem with this information if it gave me r'(t) and asked for k(t)

Thank you for your time : )

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# Curvature of a Line: Calc III

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