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).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.3: Vectors

Problem 60E

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