Let f be C1 and suppose that Df[x0] is one-to-one. Then 1. f is locally one-to-one, that

Question:

Let f be C1 and suppose that Df[x0] is one-to-one. Then
1. f is locally one-to-one, that is, there exists a neighborhood S of x0 such that f is one-to-one on S
2. f has an inverse f-1: f(S) → S that is continuous
3. f is locally onto

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Foundations of Mathematical Economics

ISBN: 978-0262531924

1st edition

Authors: Michael Carter

See More Books

Question Posted: May 02, 2016 11:51 AM

See More Questions

Let f be continuous on a closed, bounded interval [a, b] and suppose that DRf{x) exists for all x (a, b). a) Show that if f(b) < y0 < f(a), then x0 := sup{x [a, b] : f(x) > y0} satisfies f(x0) = y0...
Let C be a smooth C2 arc with parametrization (É¸, [a, b]), and suppose that s = ï¬(t) is given by (2). The natural parametrization of C is the pair (v, [0, L]), where v(s) =...
Suppose that f is C1 on an interval (a, b). If f'(x0) 0 for some x0 (a, b), prove that there exist intervals I and J such that f is 1-1 from I onto J and f-1 is continuously differentiable on J.
In a recent self-check, the store manager had her employees compare prices on 320 different items which were picked at random for cross-check. The employees recorded the shelf price and the price...
Many Americans spend time worrying about paying their bills. A survey by Fleishman-Hilliard Research for MassMutual discovered that 60% of Americans with kids say that paying bills is a major...
In Figure P3-53, calculate the temperatures at points 1, 2, 3, and 4 using the numerical method. Figure P3-53 700 C 100 C 400 C 3 500 C
Could an include use case have an include use case? Provide an example.
You have been hired as a fraud auditor to examine the assets of a company that recently filed for Chapter 11 bankruptcy. The company manufactures and sells circuit boards for childrens computerized...
Wantaby Ltd. is extending its credit terms from 45 to 60 days. Sales are expected to increase from $471 million to $5.81 million as a result Wontaby finances short-term assets at the bank at a cost...
Complete Keith's tax return including all required schedules and forms using prince edward island as province, using the fillable forms package. Taxpayers Information Taxpayer #1 Name: Keith Dox...
Compute the second-order Taylor series expansion of the quadratic Function around the point (0, 0). f(x1,x2) = ax + 2bx, x2 + cx
Let f: S n be a differentiable function on a convex set S n. Suppose that the Jacobian Jf(x) is positive (or negative) definite for all x S. Then f is one-to-one.
In Exercises 103104, use the graph of y =|4 - x| to solve each inequality. y = 5 6+ 4 3+ 2+ 1+ y = |4 -x| + + 1 2 3 4 5 6 + X + + + 7 8 9 10
A Meryl Streep and Julia Roberts vehicle depicting family dysfunction. Focus on the abundance of defensive versus supportive communication patterns and competitive and noncompetitive listening...
Can you identify any narcissistic or pathological leaders in the United States? Note the difference between emerging as a leader and exhibiting effective leadership once instated in a leadership...
What are the limitations of the decision-relevant approach?
Define a non-controllable cost.
What are the costs of holding inventory?
At 31 July 20X9, the statement of financial position of Winder Engineering plc showed the following position: The preference shares were originally issued at a premium of 10 per cent, and are...
An 8.0 kg crate is pulled 5.0 m up a 30 incline by a rope angled 18 above the incline. The tension in the rope is 120 N, and the crates coefficient of kinetic friction on the incline is 0.25. a. How...
(a) How is the inverse sine function f(x) = sin-1x defined? What are its domain and range? (b) How is the inverse cosine function f(x) = cos-1x defined? What are its domain and range? (c) How is the...
If f is a function, then f(s + t) = f(s) + f (t).
If f(s) = f (t), then s = t.
2. Consider a helicopter rotor in a wind tunnel. The rotor is spinning and the wind is turned on. The equation for the rotor flapping was derived in class for this situation. Note that = - +C/2 =...
In this problem, you are asked to go through the steps of a finite element analysis. The key features include the use of isoparametric element formulation and Gauss numerical integration. (A) Problem...
A wheel rolls without slipping on a surface with a constant radius of curvature R. The centre of curvature is located at point O. R 20 9 G m Assume the wheel can be approximated as a uniform disk...

Let f be C1 and suppose that Df[x0] is one-to-one. Then 1. f is locally one-to-one, that

Question:

Step by Step Answer:

1 Since x 0 is continuous and onetoone there exists a constant such that x 1 x 2 x ...View the full answer

Foundations of Mathematical Economics

Students also viewed these Numerical Analysis questions