Problem 1.32 Check the fundamental theorem for gradients, using T = x² + 4NN +2yz'the points a = D, and the three paths in Fig. 1.28: (0.0.0), b= ( Ka) (0.0,0)→IKI,0.0) → (1,.0)→ (1,1.1). (b) (0,0, 0) → KOJ O, 1) → (0.,1.)-110E (c) the parabolic path z = xAN=X (a) (b) (c)
Problem 1.32 Check the fundamental theorem for gradients, using T = x² + 4NN +2yz'the points a = D, and the three paths in Fig. 1.28: (0.0.0), b= ( Ka) (0.0,0)→IKI,0.0) → (1,.0)→ (1,1.1). (b) (0,0, 0) → KOJ O, 1) → (0.,1.)-110E (c) the parabolic path z = xAN=X (a) (b) (c)
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Transcribed Image Text:Problem 1.32 Check the fundamental theorem for gradients, using T =x²+
ANy +2yz' the points a = (0, 0. 0), b = (1,D, and the three paths in Fig. 1.28:
Ka) (0.0.0) → K1,0.0)→ (1,0)– (1,1,1).
(b) (0,0, 0) → KOJ 0, 1) → (0. 1! 1)÷(1:
(c) the parabolic path z = x: N=
(a)
(b)
(c)
FIGURE 1.28
Eunda mor
orom for
vorgeno
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