Question: Let f(x, y) = x2 + y, and F = {(x,y) E R? x + y > 1}. Show that f(x, y) is not

Let f(x, y) = x2 + y, and F = {(x,y) E

Let f(x, y) = x2 + y, and F = {(x,y) E R? x + y > 1}. Show that f(x, y) is not coercive on R?, and F is unbounded in R2. Further, show that f(x, y) is coercive on F, i.e., lim (x, y)EF f(x, y) = 0.

Step by Step Solution

★★★★★

3.40 Rating (150 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

ANSWER det 20 and y free in fu we get Let a0 and Hoy y Co ERY Coy EIR we h... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Show that the following tree is not arbitrage- free. Time 0 Time 1 Zero-Coupon Bond Prices B(1,3) 0.9167 B(1,2 0.9620 (Up" state) (0)-0.3 B (0,3) 0.83 B(0,2)-0.93R(O)0.0309 B(0,1) 0.97 B(1,3)0.8977...

Show that C(X) (exercise 2.85) is not an inner product space. Two vectors x and y in an inner product space X are orthogonal if xT y = 0. We symbolize this by x ¥ y The orthogonal complement...

Show that each of these is not a vector space. (Check closure by listing two members of each set and trying some operations on them.) (a) Under the operations inherited from R3, this set (b) Under...

Let f(x) = 3x + 2 / x2 + 1 and g(x) = 1/ 100 cos (100x). (a) Use functional composition to form h(x) = (f g) (x), as well as j(x) = (g f) (x). (b) Find the appropriate window or windows that give a...

'The impact of nonconstant error variance on OLS estimation: Suppose that Yi xi i, with independent errors, i ; N0; 2 i , and i xi. Let B represent the OLS estimator and b the WLS estimator of...

7. Quadratic nonresidues modulo n The set Q, of quadratic residues modulo n con- sists of those [a], Z for which we can solve x 2 = a mod n for some x with [x], Z (a) Let p be an odd prime and g a...

15. Let X1, X2, . . . , Xn represent a random sample from a Rayleigh distribution with pdf f(x; ) x e x2/(2) x 0 a. It can be shown that E(X2 ) 2. Use this fact to construct an unbiased estimator...

Hello, I am unsure how to solve this problem. Please help! Let f(x) = vx, g(x) = x2 - 2, and h(x) = . 1 X Find (fog o h) (x).

Let X1, X2, X3 be independent and identically distributed (i.i.d) random variables with the probability mass function (pmf) is f (x) = (1 - p)-p, x = 1,2,3 ... 0, otherwise, where p = -. That is, X1,...

a force 4 5 0 N is applied to a small piston of area 5 0 cm ^ 2 on a hydraulic jack. the hydraulic jack is required to lift a load 1 8 9 3 . 2 N . Calculate the area of the larger piston using...

Last month, Startup Manufacturing sold 5 5 cars of Type X for a price of $ 2 5 , 0 0 0 each, 3 0 cars of Type Y for a price of $ 3 5 , 0 0 0 each, and 1 2 cars of Type Z for a price of $ 5 0 , 0 0 0...

Problem 5. Let E, F, G be events in a probability space with sample space S and probability law Pr(), which satisfy Pr(EFG) Pr(EFG) = Pr(EFG) = Pr(EFG) = 1,4 Pr(EFG) Pr(EFG) = Pr(EFG) = Pr(EFG) = 0....

For Exercises 33-36, a function is given. (See Examples 4-5) f(x + h) f(x) a. Find f(x + h). b. Find h 33. f(x) = 5x + 9 34. f(x)=8x+4 35. f(x) = x + 4x 36. f(x) = x - 3x

Bond J has a coupon rate of 4 percent. Bond K has a coupon rate of 14 percent. Both bonds have 19 years to maturity, a par value of $1,000, and a YTM of 8 percent, and both make semiannual payments....

In a nonmagnetic medium, E = 50 cos (10 9 t 8x) a y + 40 sin (10 9 t 8x) a z V/m find the dielectric constant r and the corresponding H.

Solve 2u = 2y sin 1/3x for the grid in Fig. 461 and uy (1, 3) = uy (2, 3) = 1/2243, u = 0 on the other three sides of the square.

Rayleigh quotient why does q generally approximate the Eigen value of greatest absolute value? When will q be a good approximation?

Complexity show that Prims algorithm has complexity O(n2).

Explain the nontax similarities and differences between qualified defined contribution plans and nonqualified deferred compensation plans from an employee's perspective.

From a tax perspective, how would a taxpayer determine whether they should contribute to a traditional 401(k) or a Roth 401(k)?

How can companies use deferred compensation to avoid the 162(m) limitation on salary deductibility?