

Ex 2 6oaph & Grncet Al), Bl,3), c(3, 1). XY) X-3, y 2) Reflect X=-3dr ne & tabel Redlept ari bek & labe...
Which of the following is solution for (x^2 + y^2) dx +2xydy= 0? xy^2+1/3x^3=c x^2y+1/3x^3=c xy^2+1/2x^3=c x^2y+1/2x^3=c
1) Given the following iterated integral. ex/Y DA R = y = 4x, y = -xy = 8 a) (0.75 point) Sketch the bounded region R. Label your graph. b) (1.25 point) Evaluate the definite integral with the given function over the bounded region R.
16. xyty Let f(x, y) = x3 + xy + y}, g(x, y) = x3 a. Show that there is a unique point P= (a,b) on 9(x,y) = 1 where fp = 1V9p for some scalar 1. b. Refer to Figure 13 to determine whether $ (P) is a local minimum or a local maximum of f subject to the constraint. c. Does Figure 13 suggest that f(P) is a global extremum subject to the constraint? 2 0 -3 -2...
1.Find fxy(x,y) if f(x,y)=(x^5+y^4)^6.
2. Find Cxy(x,y) if C(x,y)=6x^2-3xy-7y^2+2x-4y-3
Find (,,(Xy) if f(x,y)= (x + y) fxy(x,y) = Find Cxy(x,y) if C(x,y) = 6x² + 3xy – 7y2 + 2x - 4y - 3. Cxy(x,y)=0
which of the following is a potential function for F(x,y,z)= < y2 +y?ex?,x2 + 2ye*?,xy + xy?e *V> f(x,y,z) = xyz + y2exyz f(x,y,z) = xyz + y2e*+2 b. F(x,y,z) has a potential function but it is not one of the other choices. F(x,y,z) does not have a potential function. d. f(x,y,z) = xyz + y2exZ e.
0 3-) Common probability function of x andy; flory) qalxo), AE {1982, y equili?? day al find the constant "C". bl find the marginal probability fuctions of x ad y c) Are X and Y independent a d) Plx<2) ,P ( X 7 Y) ,P(x+482) and Plx 22 (441) fud the probability.
Math 2510 Take Home 3 2. Fubini? Consider the function al Use the substitution u-xy (treating x as a constantl to evaluate x-y dy b) By comparing 1 (a) with 2 (a) you should be able to predict the value of Xydy dx (x+y) c) Do these results violate Fubini's Theaorem? Explain! Page 3 of 8
1. xy' = 3y + 3 3. (x + 1)y' - (2x + 3) y = 0
Problem 3 Solve the following differential equation : y = ex-xex) = dy + 2(1-x) x Initial condition is y col=0 ex (1 x) x2 Y (
Classify bifurcations for the system x '= a(1 − x) − xy^2 , y' = xy^2 − (a + k)y, where a > 0 and k > 0 are parameters, and sketch the bifurcation curve in the a − k space.