homework_7.pdf - I-12 EL CHAVEZ 005371811 IS 3013 HOMEWORK...

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I -12 EL CHAVEZ 005371811 IS 3013 : HOMEWORK 7 - 7.1.11 When the slope of the tangent line is zero , then there exists a semi stable equilibrium point 7.1.21 X ' X ' X o : XIX ' l ) @ x t and X - I , the derivative is positive so the equilibrium point is unstable I @ * Oi the derivative is negative so the otvilibrivm Point is stable SEfTl0N 7.2.11 any random pair IX. YI only produces one point in the state space so there cannot be a point that lies directly above another point SECTIONI.37.3.tl The graph has to pass through the origin because when x O and 4=0 . 2=0 so it needs to pass through the origin 7.3.21 at @ X O and 9=0 b) the red triangle is how to find the slope of the cutting plane x o , fish 4 YOU can count the # of boxes using the graphical method

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