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7. (5 marks) Consider a smooth function u(x, y) satisfying: Urx + Uyy + Uzy >...
(5 marks) Consider a smooth function u(x, y) satisfying: Show that u attains its maximum on the boundary àS2 (5 marks) Consider a smooth function u(x, y) satisfying: Show that u attains its maximum on the boundary àS2
Please help me solve this differential Equation show all steps Find a continuous solution satisfying +y-f(x), where f() Ji 10 { 0<r<1 > 1 and y(0) -0.
(6) Show that the semicircle C = {(x,y) = R2 | + y2 = 1, y > 0} is a 1-dimensional manifold with boundary and the hemisphere D= {(x, y, z) | 22 + y2 + z2 = 1, 2 > 0} is a 2-dimensional manifold with boundary. (7) Suppose X is an n-dimensional manifold with boundary. Let ax denote the set of points in the boundary of X. Show that ax is an (n-1)-dimensional manifold.
Use the method of maximum likelihood to find the estimator for a f(x) = {2ae-ar? X>0 elsewhere 0 â=
=T 20 marks) Consider the following PDE with boundary and initial conditions: U = Upx + ur, for 0<x< 1 and to with u(0,t) = 1, u(1,t) = 0, u(1,0) = (a) Find the steady state solution, us(1), for the PDE. (b) Let Uſz,t) = u(?, t) – us(T). Derive a PDE plus boundary and initial conditions for U(2,t). Show your working. (c) Use separation of variables to solve the resulting problem for U. You may leave the inner products...
Suppose that a consumer's utility function is u(x, y) = x, defined for all bundles such that x > 0 and y > 0. For any given positive level of utility, the corresponding indifference curve is O strictly convex. a vertical line. O a horizontal line. a line that is neither horizontal nor vertical.
Prove this proposition please. 4.2.19) Proposition. Whenever a <b, there is a smooth function f satisfying f(2)= { € (0,1), a<:<b, VIVA *> 6. For obvious reasons, such a function is called a bump function. o M Figure 61. A bump function
Repeat the flat-plate momentum analysis by replacing the equation u(x, y) ~U ( ) 0<y>$(x) using a trigonometric profile approximation: 5 = sin()
-). Solve the initial and boundary value problem: uUx=0, TE (0,), t > 0, U (0,t) = u(,t) = 0, >0, u(,0) - cos', 1€ (0,7).
1. (a) Suppose the unit step function uc(t) has a generalized derivative u(t) everywhere. Find L[u'(t)] for c > 0. What generalized function is u(t) equal to do you think?