Let A C Rn be an open set and f : A Rn a continuously differentiable 1-1
Question:
Let A C Rn be an open set and f : A→ Rn a continuously differentiable 1-1 function such that det f1 (x) ≠ 0 for all . Show that f (A) is an open set and f -1: f (A) →A is differentiable. Demonstrate also that f (b) is open for any open set B C A.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 50% (4 reviews)
For every there is an with By Theorem 211 there is an open set and a...View the full answer
Answered By
Mehwish Aziz
What I have learnt in my 8 years experience of tutoring is that you really need to have a friendly relationship with your students so they can come to you with their queries without any hesitation. I am quite hardworking and I have strong work ethics. Since I had never been one of those who always top in the class and always get A* no matter what, I can understand the fear of failure and can relate with my students at so many levels. I had always been one of those who had to work really hard to get decent grades. I am forever grateful to some of the amazing teachers that I have had who made learning one, and owing to whom I was able to get some extraordinary grades and get into one of the most prestigious universities of the country. Inspired by those same teachers, I am to be like one of them - who never gives up on her students and always believe in them!
5.00+
3+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Basic questions
-
(a) Let A C Rn be an open set such that boundary A is an (n - 1) -dimensional manifold. Show that N = AU boundary A is an -dimensional manifold with boundary. (It is well to bear in mind the...
-
Let p N, V be an open set in Rn, x, a V, and f: V R be Cp on V. If L(x; a) V and h = x - a, prove that D (a: h)+ (p - 1), (+ih: b di. f(x)-/(a) =
-
Muharraq Co. paid the following different costs in 2020: 1. $2,000,000 to acquire a machine to be used in the R&D projects. The machine has a 4- year useful life (Muharraq Co. started using the...
-
Divalent carbon species called carbenes care capable of fleeting existence. For example, methylene: CH2, is the simplest carbene. The two unshared electrons in methylene can be either spin-paired in...
-
Write a review of a scholarly article addressing "levels of conflict". Reviews should include a synopsis and your opinion of the article
-
In the manufacturing of digital recording tape, each of 24 tracks is classified as containing or not containing one or more bits in error.
-
MARRIOTT: Marketing Research Leads to Expanded Offerings Visit www.pearsonglobaleditions.com/malhotra to read the video case and view the accompanying video. Marriott: Marketing Research Leads to...
-
Ringo loves playing rock n roll music at high volume. Luciano loves opera and hates rock n roll. Unfortunately, they are next-door neighbors in an apartment building with paper-thin walls. a. What is...
-
Write a function sum_list(1) that takes as input a list 1 and outputs another list q of the same length as 1 and that contains at position j the sum of all the elements from positions 0, 1, ...j,...
-
NOTE: include a copy of your equations and equations/code with your plots 1. (50 points) A non-afterburning turbojet is being designed for operation at an altitude of 15 km and a Mach number of 1.8....
-
Let A C Rn be an open set and f : A Rn a continuously differentiable 1-1 function such that det f1 (x) 0 for all . Show that f (A) is an open set and f -1: f (A) A is differentiable. Show also that f...
-
a. Let f: Rn R be a continuously differentiable function. Show that f is not 1-1. b. Generalize this result to t the case of a continuously differentiable function f: Rn Rm with m < n.
-
In Problems 9 18, information is given about a polynomial function f whose coefficients are real numbers. Find the remaining zeros of f . Degree 4; zeros: 2 i, i
-
Harris plc began trading on 1 January 2006, preparing financial statements ended 31 December each year. During 2009, the company decided to change its accounting policy with regard to depreciation of...
-
Estimates indicate that in recent years, the poorest 40 percent of the population earned about 15 per- cent of total income in Argentina. In Brazil, the poorest 40 percent earned about 10 percent of...
-
In this exercise, we use the notation of the proof of Theorem 1 and prove \[ \oint_{C} F_{3}(x, y, z) \mathbf{k} \cdot d \mathbf{r}=\iint_{\mathcal{S}} \operatorname{curl}\left(F_{3}(x, y, z)...
-
Outline the key legislative and regulatory changes that have affected auditing since 2002.
-
What is the tangled ERISA regime, and what are the chances that Congress will unsnarl it?
-
In replacement problems the "life" of an asset is defined three ways. What are the three types, and why is the difference important?
-
Eleni Cabinet Company sold 2,200 cabinets during 2011 at $160 per cabinet. Its beginning inventory on January 1 was 130 cabinets at $56. Purchases made during the year were as follows: February . 225...
-
The SEC is concerned about the need for auditors to recognize the qualitative aspect of materiality judgments. Explain what the qualitative aspect of materiality means. List some factors that would...
-
Complete the table by: i. Defining each type of taxable transaction data provided below. ii. Listing one unique source of information for each type of taxable transaction data listed below. iii....
-
You are a partner in a CPA firm. You have a client that is being audited by the IRS. The IRS is using an indirect method of proof of his income. Your client is an attorney but not a tax attorney and...
-
Duncan Corp enters into a contract with Perry Company to sell four different products and each of the products is considered a separate performance obligation. The total price of the contract is...
Study smarter with the SolutionInn App