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(a) Let f(x, y) = x² + y². Plot the vector field Vf and the level curves of f on the same plot. (b) Do your vectors from the vector field point towards increasing values of the level curves or towards decreasing values? Is this consistent with the gradient being the direction of max increase?

(a) Let f(x, y) = x² + y². Plot the vector field Vf and the level curves of f on the same plot. (b) Do your vectors from the vector field point towards increasing values of the level curves or towards decreasing values? Is this consistent with the gradient being the direction of max increase?

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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(a) Let f(x, y) = x² + y². Plot the vector field Vf and the level curves of f on the same plot. (b) Do your vectors from the vector field point towards increasing values of the level curves or towards decreasing values? Is this consistent with the gradient being the direction of max increase?
Transcribed Image Text:(a) Let f(x, y) = x² + y². Plot the vector field Vf and the level curves of f on the same plot. (b) Do your vectors from the vector field point towards increasing values of the level curves or towards decreasing values? Is this consistent with the gradient being the direction of max increase?
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