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Problem 1.31 Check the fundamental theorem for gradients, usingT =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. Figure 1.28

Problem 1.31 Check the fundamental theorem for gradients, usingT =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. Figure 1.28

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Problem 1.31 Check the fundamental theorem for gradients, usingT =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. (a) (b) Figure 1.28
Transcribed Image Text:Problem 1.31 Check the fundamental theorem for gradients, usingT =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. (a) (b) Figure 1.28
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