formula for the curvature of a parametrized plane curve a. Show that the curvature of a...

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formula for the curvature of a parametrized plane curve a. Show that the curvature of a smooth curve r(t) = f(t)i + g(t)j defined by twice-differentiable functions x = f(t) and y = g(t) is given by the formula K= |xy - yx| (x² + 2)/2 The dots in the formula denote differentiation with respect to 1, one derivative for each dot. Apply the formula to find the curva- tures of the following curves. = b. r(t) ti + (In sin t)j, 0 < t < T c. r(t) [tan (sinh t)]i+ (In cosh ()j. formula for the curvature of a parametrized plane curve a. Show that the curvature of a smooth curve r(t) = f(t)i + g(t)j defined by twice-differentiable functions x = f(t) and y = g(t) is given by the formula K= |xy - yx| (x² + 2)/2 The dots in the formula denote differentiation with respect to 1, one derivative for each dot. Apply the formula to find the curva- tures of the following curves. = b. r(t) ti + (In sin t)j, 0 < t < T c. r(t) [tan (sinh t)]i+ (In cosh ()j.

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