MATH 4041 Lecture 35: Higher Order
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The domain of f(x,y) is the xy-plane, and values ofĀ fĀ are given in the table below.
Ā y\x | Ā 0 | Ā 1 | Ā 2 | Ā 3Ā | Ā 4 |
Ā 0 | Ā 60 | Ā 60 | Ā 61 | Ā 61 | Ā 61 |
Ā 1 | Ā 56 | Ā 54 | Ā 53 | Ā 54 | Ā 55 |
Ā 2 | Ā 54 | Ā 54 | Ā 55 | Ā 56 | Ā 55 |
Ā 3 | Ā 53 | Ā 54Ā | Ā 54 | Ā 55 | Ā 54 |
Ā 4 | Ā 55 | Ā 55 | Ā 57 | Ā 58 | Ā 57 |
Find grad , whereĀ C is
(a) A line from (1,0) to (3,3).
Ā gradĀ = -5
(b)Ā A circle of radius 1 centered at (1,2) traversed counterclockwise.
Ā gradĀ =
Ā