Detailed solution to Problem Set 10 Exercise 1

Question:
Evaluate 3x dx + 4x2y dy at (x, y) = (2, 6) along ⟨dx, dy⟩ = ⟨0.003, 0.005⟩.
Solution:
(3x dx + 4x2y dy)|(x, y)=(2, 6), ⟨dx, dy⟩=⟨0.003, 0.005⟩ = 3(2)(0.003) + 4(2)2(6)(0.005) = 0.498.

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