a. Show that when you express ds 2 = dx 2 + dy 2 + dz 2

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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 = e^θ, z = e^θ, 0 ≤ θ ≤ ln 8.

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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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Question Posted: May 08, 2023 03:39 AM

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a. Show that when you express ds 2 = dx 2 + dy 2 + dz 2

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a To express ds2 dx2 dy2 dz2 in terms of cylindrical coordinates we need to substitute the relations...View the full answer

Thomas Calculus Early Transcendentals

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