Let r = xi + yj + zk and let r = |r|. a. Show that r

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Let r = xi + yj + zk and let r = |r|.

a. Show that ∇r = r/r.

b. Show that ∇(rⁿ) = nrⁿ^-2r.

c. Find a function whose gradient equals r.

d. Show that r · dr = r dr.

e. Show that ∇(A · r) = A for any constant vector A.

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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 09, 2023 05:10 AM

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Let r = xi + yj + zk and let r = |r|. a. Show that r

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Step by Step Answer:

a We have r r x2 y2 z212 Taking the gradient of r we get r rxi ryj rzk 122xx2 y2 z...View the full answer

Thomas Calculus Early Transcendentals

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