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By about how much will f(x,y,z) = In √√x² + y² +z² change if the point P(x,y,z) moves from Po(4,1,3) a distance of ds = 0.1 unit in the direction of 3i+6j-2k? The change in value is about df (Round to four decimal places.) www

By about how much will f(x,y,z) = In √√x² + y² +z² change if the point P(x,y,z) moves from Po(4,1,3) a distance of ds = 0.1 unit in the direction of 3i+6j-2k? The change in value is about df (Round to four decimal places.) www

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Question:** By about how much will \( f(x, y, z) = \ln \sqrt{\frac{x^2 + y^2 + z^2}{2}} \) change if the point \( P(x, y, z) \) moves from \( P_0(4, 1, 3) \) a distance of \( ds = 0.1 \) unit in the direction of \( 3\mathbf{i} + 6\mathbf{j} - 2\mathbf{k} \)? --- **Instruction:** The change in value is about \( df \approx \underline{\hspace{2em}} \). (Round to four decimal places.)
Transcribed Image Text:**Question:** By about how much will \( f(x, y, z) = \ln \sqrt{\frac{x^2 + y^2 + z^2}{2}} \) change if the point \( P(x, y, z) \) moves from \( P_0(4, 1, 3) \) a distance of \( ds = 0.1 \) unit in the direction of \( 3\mathbf{i} + 6\mathbf{j} - 2\mathbf{k} \)? --- **Instruction:** The change in value is about \( df \approx \underline{\hspace{2em}} \). (Round to four decimal places.)
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