II. Determine and interpret the curvature K of the curve at the value of the given parameter a) \(r(t) = t^2i + j; t = 2\) b) \(r(t) = (3t, 2t^2)\) en el punto \((-3,2)\) c) \(r(t) = ti + t^2j + \frac{t^3}{4}k; t = 2\)
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For the first curve, rt = ti + jt = 2, we can find the curvature using the formula: K = |rt' x rt''| / |rt'|^3 First, let's find rt' and rt'': rt' = d(rt)/dt = d(ti + jt)/dt = i + j rt'' = d(rt')/dt = d(i + j)/dt = 0 Now, let's find |rt' x rt''| and Show more…
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