a. Show that when you express ds 2 = dx 2 + dy 2 + dz 2
Question:
a. Show that when you express ds2 = dx2 + dy2 + dz2 in terms of cylindrical coordinates, you get ds2 = dr2 + r2 dθ2 + dz2.
b. Interpret this result geometrically in terms of the edges and a diagonal of a box. Sketch the box.
c. Use the result in part (a) to find the length of the curve r = eθ, z = eθ, 0 ≤ θ ≤ ln 8.
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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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