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Question 26 1 pts Use the Fundamental Theorem of Line Integrals (FTLI) to evaluate the given integral. Let F = < yz, xz, xy). Find the work done by this force field on an object moving from (1,1,1) to (4,4,4). O 54 57 60 o oo 63
( xy 7. CHALLENGE: fxy(x, y) = 0< < 2, 0 <y <1 otherwise 0 Find P(X+Y < 1) HINT: consider the region of the XY plane where the inequality is true.
1. Let E = {(1, y) ERP|0< + y2 <1}U{(2,0)}. Give the following sets: Eº, Ē, E°, Ē°, DE, DE, and a E.
6. Let a curve be parameterized by x = t3 – 9t, y=t+3 for 1 st < 2. Find the xy coordinates of the points of horizontal tangency and vertical tangency.
Let X, Y be jointly continuous with joint density function (pdf) fx,y(x, y) *(1+xy) 05 x <1,0 <2 0 otherwise (a) Find the marginal density functions (pdf) fx and fy. (b) Are X and Y independent? Why or why not?
(7 pts.) Let f(x, y, z) = "y and let R be the region {(x, y, z) |2 < x < 4,0 Sy < 3,15 zse}. 2 Evaluate | $180,0,.2) av. R
3. (15 pts) Let D be an infinite set with cardinal d. Let A = {X C D | 0(X) <3}. Prove that o(A) = d.
Question 1 1 pts Let F= (2,0, y) and let S be the oriented surface parameterized by G(u, v) = (u? – v, u, v2) for 0 <u < 12, -1 <u< 4. Calculate | [F. ds. (enter an integer) Question 2 1 pts Calculate (F.ds for the oriented surface F=(y,z,«), plane 6x – 7y+z=1,0 < x <1,0 Sysi, with an upward pointing normal. (enter an integer) Question 3 1 pts Calc F. ds for the oriented surface F =...
D Question 11 12 pts to Consider the vector field F (x, y, z) =< 2x – yz, 2y – az,2z – xy>. a) (3) Is this vector field conservative? Justify your answer. b) (9) Find the amount of work done by this vector field in moving a particle along the curve (t) =< 3cost, cos’t, cos” (2t) > from t = 0 tot = 1
1. Consider y(t) = Sant – 7)e(r)dr, -20 <t<oo. Compute y(t) given: z(t) = 6(t)e- - u(t), and h(t) 2 Habaq 1 1 1 2 3