a. The graph y = (x) in the xy-plane automatically has the parametrization x = x, y
Question:
a. 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, then
b. Use the formula for k in part (a) to find the curvature of y = ln (cos x), -π/2
c. Show that the curvature is zero at a point of inflection.
Exercise 1
Find T, N, and κ for the plane curves.
r(t) = ti + (ln cos t)j, -π/2
Transcribed Image Text:
. 7/ε [z((x), f) + 1] |(x) uf| K(X) =
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Related Book For
Thomas Calculus Early Transcendentals
ISBN: 9780321884077
13th Edition
Authors: Joel R Hass, Christopher E Heil, Maurice D Weir
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