Question 3 Evaluate Sſezx=3> 22x+3y dĀ where R is the region bounded by x = 0, y = 0 and x + y =1. (10 marks) R
Let z=5 where x, y, z E R. Prove that z? +z2+z?>
Evaluate SS Pods where È CM,y,z) = 5 zex, sy, 2-yz?> s is the where s suface of the unit cube in IR R? not including the face Z-0.
17.3 Evaluate the following integral: SSR cosh(x + y)dA where R is the region bounded by x > 0, y = 0 and the line x + 2y = 2.
2. Shade the region of the complex plane defined by <z +4 + 3i : 3 < 3 < 5,2 EC}. Include the appropriate axis labels and any significant points.
(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
4. Let {Sn,n > 0} be a symmetric Random Walk on Z. with So-0. Defined Y, max{Sk, 1 3 k S nt, for n 2 0, prove, thanks to a counterexample, that Y is not a Markov Chain
3. (a) (5 points) On the set A= R\{0}, let x ~ y if and only if x · y > 0. Is this relation an equivalence relation? Prove your answer. (b) (5 points) Let B = {1, 2, 3, 4, 5} and C = {1,3}. On the set of subsets of B, let D ~ E if and only if DAC = EnC. Is this relation an equivalence relation? Prove your answer.
Assume that x =5, y = 6, and z = -3. What is the value of the expression: y >= 6 && z < -1 Answer:
in each case: (e) Compute y = sin(z)cos(r) for 0 < z < π/2