(5) Let 2 := {(r, y) E R | 1 < r + y < 4}...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
(5) Let 2 := {(r, y) E R² | 1 < r² + y < 4} be a punctured disc and let f: 0R be a continuous function which is "locally convex" (that is for every point r in the interior of N there is a small open ball on which f is convex). Suppose that the maximum of f on 2 occurs at an interior point ro of 2. Prove that f must be a constant function on 2. (5) Let 2 := {(r, y) E R² | 1 < r² + y < 4} be a punctured disc and let f: 0R be a continuous function which is "locally convex" (that is for every point r in the interior of N there is a small open ball on which f is convex). Suppose that the maximum of f on 2 occurs at an interior point ro of 2. Prove that f must be a constant function on 2.
Expert Answer:
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
In the interior of a sphere of radius 1 kept at the potential f(Ф) = cos 2 Ф + 3 cos Ф (referred to our usual spherical coordinates).
-
Let f be a convex function on an open set S that is bounded above by M in a neighborhood of x0; that is, there exists an open set f containing x0 such that f(x) ¥ M for every x U 1. Show that...
-
Let f be a convex function on an open set S which is bounded above by M in a neighborhood of x0. That is, there exists an open ball Br(x0) containing x0 such that f is bounded on B(x0). Let x1 be an...
-
The people on Coral Island buy only juice and cloth. The CPI market basket contains the quantities bought in 2016. The average household spent $60 on juice and $30 on cloth in 2016 when the price of...
-
In the chapter, we mentioned that many companies have been under pressure to declassify their boards of directors. Why would investors want a board to be declassified? What are the advantages of a...
-
Is the amount of money spent by companies on advertising a function of the total revenue of the company? Shown are revenue and advertising cost data for nine companies published by Advertising Age....
-
Whalen Company manufactures tablecloths. Sales have grown rapidly over the past 2 years. As a result, the president has installed a budgetary control system for 2002. The following data were used in...
-
Kaelea, Inc., has no debt outstanding and a total market value of $70,000. Earnings before interest and taxes, EBIT, are projected to be $6,000 if economic conditions are normal. If there is strong...
-
Question 34 Not yet answered Marked out of 1 Flag question The accounting equation that proves correct and follows in the balance sheet is a. None of these. Ob. Revenue-Expenses Net Income c. Assets...
-
On May 1, a petty cash fund was established for $150.00. The following vouchers were issued during May: REQUIRED 1. Prepare the journal entry to establish the petty cash fund. 2. Record the vouchers...
-
1.) Prepare statement of Comprehensive Income from the information given below of ABC SAOC for the year ended 31st December 2018: Sales Revenue Cost of sales 38,277,238 27,721,482 Gross profit...
-
X1036: Contains Two The following method takes in a List of generic parameter type T and a value of the same type. This method should return true if there are at least two occurrences of value in the...
-
discuss how SAS 99 can be used when looking for fraudulent transactions as it pertains to payroll.
-
For most companies, payroll is a major cost of operations. An auditor is routinely required to audit the payroll function and to look for fraud. Please discuss how SAS 99 can be used when looking for...
-
The Income Statement and Balance Sheet consistently tell a financial story. That story has many chapters and can change dramatically based upon macroeconomic conditions. Locate the Form 10-K of a...
-
Territory and Product Profitability Analysis Pipeline Surfboards Inc. manufactures and sells two styles of surfboards, Atlantic Wave and Pacific Pounder. These surfboards are sold in two regions,...
-
1. The following is the post-closing trial balance for the Whitlow Manufacturing Corporation as of December 31, 2023. Account Title Cash Accounts receivable Inventory Equipment Accumulated...
-
l ask this second time correnct answer is 38,01 can we look pls Consider a non-conducting rod of length 8.8 m having a uniform charge density 4.5 nC/m. Find the electric potential at P, a...
-
What is unusual about glutathione's structure? (If you can't answer this question, draw the structure you would expect for a tripeptide of glutamate, cysteine, and glycine, and compare your structure...
-
How many bonding, nonbonding, and antibonding molecular orbitals does cyclobutadiene have? In which molecular orbitals are the electrons?
-
For each of the following compounds, shown in their acidic forms, draw the form in which it will predominate in a solution of pH = 7: a. CH3COOH (pKa = 4.76) c. H3O+ (pKa 1.7) d. CH3CHOH (pKa 15.9)...
-
Using the data in BE3-1 1, prepare the cost section of port for Motta Company.
-
Data for Madlock Company are given in BE3-8. Production records indicate that 18,000 units were transferred out, and 2,000 units in ending work in process were 50% complete as to conversion cost and...
-
Mary Lou Company manufactures pizza sauce through two production depart- Journalize transactionsents: Cooking and Canning. In each process, materials and conversion costs are incurred evenly...
Study smarter with the SolutionInn App