
3. Suppose x,y,z satisfy the competing species equations <(6 - 2x – 3y - 2) y(7 - 2x - 3y - 22) z(5 - 2x - y -22) (a) (6 points) Find the critical point (0,Ye, ze) where ye, we >0, and sketch the nullclines and direction arrows in the yz-plane. (b) (6 points) Determine if (0, yc, ze) is stable. (c) (8 points) Determine if the critical point (2,0,0) is stable, where I > 0.
U Question 22 1 pts Find the absolute minimum of f(x, y) = x2 + 4y? - 2x²y + 4 on the square given by -1 << < 1 and -1<y<1. 11 4 8 None of the above or below O-2 07
the answer should be 4/3 x
u Lipulation of X given Y =y? 10. Let X and Y have joint density (2xy for 0 Sy < 2x < 2 f(x, y) = { otherwise. What is the conditional expectation of Y given X = r?
(-2<x<3 21 Graph the feasible region for the system-15y 35 (2x + y<6
Solve the system of inequalities by graphing.
X y < 2x-3 (y24
Find the absolute maximum and minimum values of f(x,y) = 2x + y4 on the set D = {(x,y) x2 + y2 <1}.
(3x + y 55 (9 pts) 4. Use the simplex method to maximize p= 2x + y, subject to <x+2y 52 x 20,y20
Question 7 (5 points) Let f(x) = 24 and -2x, x < 5 9 3 22, x > 5 Evaluate(gof)(7) A/
Solve the inequality. 2x + 3 -1< 5
Prove the statement is true.
(a) The set A= {(2,y) ERR:22 + y2 <1} is uncountable.