a. Let f: Rn R be a continuously differentiable function. Show that f is not 1-1. b.
Question:
b. Generalize this result to t the case of a continuously differentiable function f: Rn → Rm with m < n.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 40% (5 reviews)
We will show the result is true even if is only defined in a nonempty open subset of Following the h...View the full answer
Answered By
Ayush Mishra
I am a certified online tutor, with more than 3 years of experience in online tutoring. My tutoring subjects include: Physics, Mathematics and Mechanical engineering. I have also been awarded as best tutor for year 2019 in my previous organisation. Being a Mechanical Engineer, I love to tell the application of the concepts of science and mathematics in the real world. This help students to develop interest and makes learning fun and easy. This in turn, automatically improves their grades in the subject. I teach students to get prepared for college entry level exam. I also use to teach undergraduate students and guide them through their career aim.
5.00+
2+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Basic questions
-
(3) (5 marks.) Let A = where i, da/dt. (a) Find a matrix P that diagonalizes A. (b) Using the results in (a) solve the system of ODES, -3 0-4 -2 2-1 203 = = -3x1 - 4x3, = 1 3 U -2x1 + 2x2 - 13,...
-
Show that X t is not a martingale.
-
Show that is not associative. That is, show that (A B) C is not equivalent to A (B C).
-
Draw and name the eight isomeric alcohols with formula C5H12O.
-
Write a paper on "Job Search as a System Security Engineer". It's an Introduction and methodology, action research paper
-
Which compound in each of the following pairs would you expect to have the more polar carbonmetal bond? Compare the models on Learning By Modeling with respect to the charge on the carbon bonded to...
-
Determine the present worth of 5 equal annual deposits of \($1\),200 at the end of years 1 through 5, followed by 4 equal annual withdrawals of \($700\) at the end of years 4 through 7. Note that...
-
A meeting of your accounting department is scheduled for early tomorrow morning. One topic of discussion is certain to be the appropriate adjustments to net income in your company's statement of cash...
-
A large shareholder owned furniture company known for its trendy, but low-priced merchandise has been the target of criticism for its environmental practices. For example, an article an influential...
-
Consider the following income tax footnote information for Oracle for the fiscal year ended May 31, 2019 (fiscal year 2019). The following is a geographical breakdown of income before the provision...
-
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...
-
a. If f : R R satisfies f1 (a) 0 for all a R, show that f is 1-1 on all of R.
-
Use conditional proof and the eighteen rules of inference to derive the conclusions of the following symbolized arguments. Having done so, attempt to derive the conclusions without using conditional...
-
You have a rigid container of volume 0.01 m 3 that you wish to contain water at its critical point. To accomplish this task, you start with pure saturated water at 1 bar and heat it. (a) How much...
-
Prepare trading and profit and loss account and balance sheet from the following particulars as on March 31, 2005. Closing stock Rs. 30,000. Account Title Purchases and Sales Return inwards and...
-
Alphas balance-of-payments data for 2010 are shown below. All figures are in billions of dollars. What are the (a) balance on goods, (b) balance on goods and services, (c) balance on current account,...
-
Suppose that annual output in year 1 in a 3-good economy is 3 quarts of ice cream, 1 bottle of shampoo, and 3 jars of peanut butter. In year 2, the output mix changes to 5 quarts of ice cream, 2...
-
Prepare trading and profit and loss account and balance sheet of M/s Royal Traders from the following balances as on March 31, 2005. Closing stock Rs.8,000 Debit balances Stock Cash Bank Carriage on...
-
If cyclic boundary conditions are imposed on a periodic 1D lattice by identifying the two ends with \(N\) cycles between the boundaries, the translation group becomes a cyclic group of order \(N\)....
-
Linda Lopez opened a beauty studio, Lindas Salon, on January 2, 2011. The salon also sells beauty supplies. In January 2012, Lopez realized she had never filed any tax reports for her business and...
-
Auditors base materiality on quantitative factors, but not qualitative factors. (T/F)
-
QUESTION 29 Kendall's support for the current tax year came from the following sources: Kendall's wages $9,000 (Kendall spent $7,000 of these funds.) Kendall's father $ 4,500 Nontaxable scholarships...
-
In the era of Covid 19 changed hospitality and created more opportunity than ever- now is the time for innovation!!!.... Create a new hospitality endeavor (restaurant, hotel, etc.) and describe the...
-
Macintyre says "the distinction between civil and criminal law is fundamental to English Law" with reference to this statement discuss the various differences between civil and criminal law. ?
Study smarter with the SolutionInn App