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

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Homework 8 SolutionsTotal points: 42March 12, 2020Section 7.4 ExercisesEx 7.4.1 (2 pts)Solution:On the left, we have shown the graph ofZ=X2+Y2; 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)
2
Ex 7.4.6 (2 pts)
Ex 7.4.7 (2 pts)
3
Section 7.4 Further ExercisesFE 7.4.2 (6 pts)Solution:1.@f@Y=-3Y2+ 2X3.@u@s= 10s-3t3.@r@P= 3 + 6NP+ 2e2PFE 7.4.3 (2 pts)Solution:@f@X= 10X-12X2Y5@f@Y= 6Y2-20X3Y44
FE 7.4.6 (12 pts)Solution:a)@f@X= 5Y-6X@f@Y= 5X-2Yb)@f@X(1,2)= 4@f@Y(1,2)= 1c)Δf4·ΔX+ 1·ΔYd)f(X, Y)-f(1,2)4(X-1) + 1(Y-2)f(X, Y)4(X-1) + 1(Y-2) + 3f(X, Y)4X+Y-3e)f(0.97,2.06)4·0.97 + 2.06-3 = 2.94f) The tangent plane at (1,2,3) isZ= 4X+Y-3.5
Section 7.5 ExercisesEx 7.5.1 (2 pts)

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Jac, Equilibrium point, Stability theory

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