Question: Check the fundamental theorem for gradients, using T = x2 + 4xy + 2yz3, the points a = (0, 0, 0), b = (1, 1,

Check the fundamental theorem for gradients, using T = x2 + 4xy + 2yz3, the points a = (0, 0, 0), b = (1, 1, 1), and the three paths in Fig. 1.28:?

(a) (0,0.0) ??? (1.0, 0) ??? (1, 1,0) ??? (1, 1.1);?

(b) (0,0.0) ??? (0,0, 1) ??? (0, 1, 1) ??? (1, 1, 1);?

(c) the parabolic path z = x2; y = x.

2 y (a) y (b)

2 y (a) y (b)

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