LS 30B2-3 Homework 8 Solutions.pdf - Homework 8 Solutions...

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Homework 8 Solutions Total points: 42 March 12, 2020 Section 7.4 Exercises Ex 7.4.1 (2 pts) Solution: On the left, we have shown the graph of Z = X 2 + Y 2 ; on the right, we have shown the graph near the point (1 , 1 , 2). As we zoom in, the surface around the point appears flatter and flatter. In other words, as we zoom in, the surface will be approximated by the tangent plane at (1 , 1 , 2) better and better. 1
Ex 7.4.2 (2 pts)
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Ex 7.4.6 (2 pts)
Ex 7.4.7 (2 pts)
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Section 7.4 Further Exercises FE 7.4.2 (6 pts) Solution: 1. ∂f ∂Y = - 3 Y 2 + 2 X 3. ∂u ∂s = 10 s - 3 t 3. ∂r ∂P = 3 + 6 NP + 2 e 2 P FE 7.4.3 (2 pts) Solution: ∂f ∂X = 10 X - 12 X 2 Y 5 ∂f ∂Y = 6 Y 2 - 20 X 3 Y 4 4
FE 7.4.6 (12 pts) Solution: a) ∂f ∂X = 5 Y - 6 X ∂f ∂Y = 5 X - 2 Y b) ∂f ∂X (1 , 2) = 4 ∂f ∂Y (1 , 2) = 1 c) Δ f 4 · Δ X + 1 · Δ Y d) f ( X, Y ) - f (1 , 2) 4( X - 1) + 1( Y - 2) f ( X, Y ) 4( X - 1) + 1( Y - 2) + 3 f ( X, Y ) 4 X + Y - 3 e) f (0 . 97 , 2 . 06) 4 · 0 . 97 + 2 . 06 - 3 = 2 . 94 f) The tangent plane at (1 , 2 , 3) is Z = 4 X + Y - 3 . 5
Section 7.5 Exercises Ex 7.5.1 (2 pts)

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