Suppose that V is open in Rn, that f V R is C2 on V, and that fxj(a) 0 for some a H and all j I, ,n Prove that if H is a compact convex subset of V, then there is a constant M such that for all x H If (x) f (a) M x a 2

Question: Suppose that V is open in Rn, that f: V R is C2 on V, and that fxj(a) = 0 for some a H and

Suppose that V is open in Rn, that f: V †’ R is C2 on V, and that fxj(a) = 0 for some a ˆˆ H and all j = I, ...,n. Prove that if H is a compact convex subset of V, then there is a constant M such that

for all x ˆˆ H.

If (x) f (a) < M|x - a||2

Step by Step Solution

★★★★★

3.30 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Let x H Since H is convex use Taylors Formula to write fx ... 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

Document Format (1 attachment)

741-M-N-A-D-I (665).docx

120 KBs Word File

Students Have Also Explored These Related Numerical Analysis Questions!

The following selected accounts and their current balances appear in the ledger of Clairemont Co. for the fiscal year ended May 31, 2016: Cash Accounts Receivable Inventory Estimated Returns...

Suppose that V is open in Rn, that f, g: V R3, and that a V. If f and g are differentiable at a, prove that f g is differentiable at a and D(f g)(a)(y) = f(a) (Dg(a)(y)) - g(a) (Df(a)(y)) for...

Suppose that V is open in Rn, that a V, and that F : V R is C1 on V. If F(a) = 0 Fxj(a) and u(j): = (x1 . . . . .. . . .-xj-1, xj+1,. . . . . . . . ., xn) for j = 1,2, ...,n, prove that there exist...

Suppose that V is open in Rn and that f: V R is continuous. Prove that if for all nonempty Jordan regions E V, then f = 0 on V. L sav f dV = 0

7. Suppose that V is open in Rn , f: V -+ R is C2 on V, and fxJa) = for some a E V and all j = 1, ... , n. Prove that if H is a compact convex subset of V, then there is a constant M such that for...

Suppose that A is open in Rn and f: A Rm. Prove that f is continuous on A if and only if f-l (V) is open in Rn for every open subset V of Rm.

10. Suppose that V is open in Rn and 1 : V --+ R is continuous. Prove that if L I(x) d:i; = 0 for all nonempty Jordan regions E c V, then 1 = 0 on V.

10. Let E be a set in Rm. For each u : E --+ R that has second-order partial derivatives on E, Laplace's equation is defined by m {)2U ~u:= L () 2 x j=l J (a) Show that if u is C2 on E, then ~u = 'V....

Let E be a set in Rm. For each u: E R which has second-order partial derivatives on E, Laplace's equation is defined by a) Show that if u is C2 on E, then Îu = (u) on E. b) Show that if E R3...

Let V be open in Rn, a V, f : V R, and suppose that f is differentiable at a. a) Prove that the directional derivative Duf(a) exists (see Exercise 11.2.10) for each u Rn such that ||u|| = 1 and...

7. Let V be open in Rn, a E V, f: V -+ R, and let f be differentiable at a. (a) Prove that the directional derivative Duf (a) exists (see Exercise 9, p. 338), for each u E Rn such that Ilull = 1, and...

The following letter has errors in spelling, proofreading, verbs, sentence structure, parallelism, and other writing techniques studied in this chapter. You may either (a) Use standard proofreading...

Determine the avarage value for f(x)=8x-3+5e2-x on on [0,2].

A manufacturer can choose to operate under cGMP regulations under 2 1 CFR 2 1 0 and 2 1 1 for its single - entity or co - packaged drug device combination product. The manufacturer would also have to...

identify the success factors of the Amazon mobile business model?

In October 2019, Renee finally realized her dream of opening her own business, Renees Cakes and Ice Cream, LLC. Renee is the sole owner but she does employee part-time help. Renees Cakes and Ice...

how did virginia Oyeronke Oyewumi used her beliefs and principles in bringing change in the society?

A wooden bar of 8 m long, 100 mm wide and 120 mm thick is subjected to an action pull of 50 kN and stretch is 4 mm. Calculate value of strain for the material a. Stress b. Strain c. Modulus of...

A question that sways a respondent to answer in a desired manner is a .

Use regression to estimate the acceleration at each time for the following data with second-, third-, and fourth-order polynomials. Plot theresults. 2 3.25 4.5 6 7. 8.5 9.3 10 14 10 1 11 14 17 16 12...

You have to measure the flow rate of water through a small pipe. In order to do it, you place a bucket at the pipes outlet and measure the volume in the bucket as a function of time as tabulated...

The velocity (m/s) of air flowing past a flat surface is measured at several distances y (m) away from the surface. Determine the shear stress (N/m 2 ) at the surface ( y = 0), Assume a value of...

The YMCA would like to administer a satisfaction survey to its current members. The YMCA administration would like to ask a sample of 50 members about their level of satisfaction with the YMCA.You...

Imagine that a car dealership is collecting data on the individuals who buy their cars. Identify a potential categorical variable that they could collect

HotFoot Shoes would like to maintain its cash account at a minimum level of $42,000 but expects the standard deviation in net daily cash flows to be $3,700, the effective annual rate on marketable...