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Let g: R² → R be given by g(x, y) = e-y²+z-2 (a) Explain in words the difference between a contour and a cross section. (b) Find the contours of g for heights 1, e, and e². (c) Sketch the contours from (b) on a single labelled diagram. (d) Without finding Vg, mark the direction of Vg at three points on the e contour you drew in part (c). (e) Without finding Vg, mark the direction in which the directional derivative is 0 at three points on the e² contour you drew in part (c).

Let g: R² → R be given by g(x, y) = e-y²+z-2 (a) Explain in words the difference between a contour and a cross section. (b) Find the contours of g for heights 1, e, and e². (c) Sketch the contours from (b) on a single labelled diagram. (d) Without finding Vg, mark the direction of Vg at three points on the e contour you drew in part (c). (e) Without finding Vg, mark the direction in which the directional derivative is 0 at three points on the e² contour you drew in part (c).

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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Let g: R² → R be given by g(x, y) = e-y²+x-2 (a) Explain in words the difference between a contour and a cross section. (b) Find the contours of g for heights 1, e, and e². (c) Sketch the contours from (b) on a single labelled diagram. (d) Without finding Vg, mark the direction of Vg at three points on the e contour you drew in part (c). (e) Without finding Vg, mark the direction in which the directional derivative is 0 at three points on the e² contour you drew in part (c).
Transcribed Image Text:Let g: R² → R be given by g(x, y) = e-y²+x-2 (a) Explain in words the difference between a contour and a cross section. (b) Find the contours of g for heights 1, e, and e². (c) Sketch the contours from (b) on a single labelled diagram. (d) Without finding Vg, mark the direction of Vg at three points on the e contour you drew in part (c). (e) Without finding Vg, mark the direction in which the directional derivative is 0 at three points on the e² contour you drew in part (c).
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