The formula derived in Exercise 5, expresses the curvature k(x) of a twice-differentiable plane curve y =

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The formulaimage


derived in Exercise 5, expresses the curvature k(x) of a twice-differentiable plane curve y = ƒ(x) as a function of x. Find the curvature function of each of the curves. Then graph ƒ(x) together with k(x) over the given interval. You will find some surprises.



y = sin x, 0 ≤ x ≤ 2π



Data from Exercise 5


The graph y = ƒ(x) in the xy-plane automatically has the parametrization x = x, y = ƒ(x), and the vector formula r(x) = xi + ƒ(x)j. Use this formula to show that if ƒ is a twice-differentiable function of x, thenimage


Use the formula for κ in part (a) to find the curvature of y = ln (cos x), -π/2

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Thomas Calculus Early Transcendentals

ISBN: 9780321884077

13th Edition

Authors: Joel R Hass, Christopher E Heil, Maurice D Weir

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