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4.97 The function z(x, y) at the point (0, 0) lo has a gradient 4î + 6j. .oor a bvsH (a) What is the derivative in the direc- tion pointing toward (2, 3)? Isi. noo (b) What is the derivative in the direc- Tasieno tion pointing toward (-2,-3)? 1o (c) If you put a ball down on this surface at the point (0, 0), which way would it roll?

4.97 The function z(x, y) at the point (0, 0) lo has a gradient 4î + 6j. .oor a bvsH (a) What is the derivative in the direc- tion pointing toward (2, 3)? Isi. noo (b) What is the derivative in the direc- Tasieno tion pointing toward (-2,-3)? 1o (c) If you put a ball down on this surface at the point (0, 0), which way would it roll?

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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4.97 The function z(x, y) at the point (0, 0) to has a gradient 4î + 6. (a) What is the derivative in the direc- .mosA bsHo(d) h tion pointing toward (2, 3)? lsi. n00 (b) What is the derivative in the direc- Taslerios tion pointing toward (-2,-3)? lo (c) If you put a ball down on this surface at the point (0, 0), which way would it roll? (d) Find a unit vector (magnitude of 1) for which D, = 0. (e) For how many other unit vectors does D, = 0?
Transcribed Image Text:4.97 The function z(x, y) at the point (0, 0) to has a gradient 4î + 6. (a) What is the derivative in the direc- .mosA bsHo(d) h tion pointing toward (2, 3)? lsi. n00 (b) What is the derivative in the direc- Taslerios tion pointing toward (-2,-3)? lo (c) If you put a ball down on this surface at the point (0, 0), which way would it roll? (d) Find a unit vector (magnitude of 1) for which D, = 0. (e) For how many other unit vectors does D, = 0?
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