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, thenimage


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

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For  book-img-for-question

Thomas Calculus Early Transcendentals

ISBN: 9780321884077

13th Edition

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

Question Posted: