Suppose that a Rn that L Rm, and that f: Rn Rm. Prove that

Question:

Suppose that a ∈ Rn that L ∈ Rm, and that f: Rn → Rm. Prove that if f(x) → L as x → a, then there is an open set V containing a and a constant M > 0 such that ||f(x)|| < M for all x ∈ V.

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

Step by Step Answer:

Related Book For book-img-for-question

An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

See More Books

Question Posted: Mar 29, 2016 04:14 AM

See More Questions

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.
Suppose that A is closed in Rn and f: A Rm. Prove that f is continuous on A if and only if f-l (E) is closed in Rn for every closed subset E of Rm.
Suppose that E Rn and that f: E Rm. a) Prove that f is continuous on E if and only if f-1(B) is relatively closed in E for every closed subset B of Rm. b) Suppose that f is continuous on E. Prove...
E-max sold Dishwashers on credit, worth OMR 55,000 to customers, out of these Dishwashers customers return damaged Dishwashers for OMR 6,000. Record the entry for the Dishwashers returned? a. Debit...
Quantum Moving Company has the following data. Industry information also is shown. As an industry analyst comparing the firm to the industry, are you likely to praise or criticize the firm in terms...
Fill in the blanks: The ___________________ access modifier allows access to everything the ___________________ access modifier does and more. A. package-private, private B. private, protected C....
Table B. 15 presents data on air pollution and mortality. Use the all-possibleregressions selection on the air pollution data to find appropriate models for these data. Perform a thorough analysis of...
Stewart Recording Studio, owned by Ron Stewart, showed the following bank reconciliation at March 31: A list of deposits made and cheques written during April, taken from the Cash Receipts Journal...
J. Clancy owns Clancy Consulting. On December 31 of the prior year, the Retained Earnings account balance was $27,000. During the current year, the company paid $13,800 in cash dividends. Clancy...
Francis Company owns equipment that cost $50,000 when purchased on January 1, 2011. It has been depreciated using the straight-line method based on estimated salvage value of $8,000 and an estimated...
A polynomial on Rn of degree N is a function of the form where aj1 jn are scalars, N1,..., Nn are nonnegative integers, and N = N1 + N2 + + Nn. Prove that if P is a polynomial on Rn and a Rn, then...
Suppose that a = (a1 an) Rn, that fj: R R for j = 1, 2,..., n, and that g(x1, x2,..., xn) := f1(x1) fn(xn). a) Prove that if fj(t) fj(a) as t aj, for each j = 1,..., n, then g(x) f1(a1) ...
1. Discuss the practice of selling upgrades as a mechanism design. 2. What dual objectives are being served when a breakthrough new product is not equipped with all its known value added features? 3....
You are standing on a straight stretch of road and watching the motion of a bicycle; you choose your position as the origin. At one instant, the position of the bicycle is negative and its velocity...
You throw a rock upward. The rock is moving upward, but it is slowing down. If we define the ground as the origi n, the position of the rock is __ and the velocity of the rock is __ . A. positive,...
Black vultures excel at gliding flight; they can move long distances through the air without flapping their wings while undergoing only a modest drop in height. A vulture in a typical glide in still...
II Weddell seals make holes in sea ice so that they can swim BIO down to forage on the ocean floor below. Measurements for one seal showed that it dived straight down from such an opening, reaching a...
A car travels to the left at a steady speed for a few seconds, then brakes for a stop sign. Use the particle model to draw a motion diagram of the car for the entire motion described here. Number the...
Shielded rooms act as resonant cavities. We must avoid operating equipment in any such room at a resonant frequency of the cavity. If an air-filled shielded room has the dimensions 10.2 m by 8.7 m by...
Represent each of the following combination of units in the correct SI form using an appropriate prefix: (a) m/ms, (b) k m, (c) k s /mg, and (d) k m N.
A manufacturer of semiconductor devices takes a random sample of size n of chips and tests them, classifying each chip as defective or non-defective. Let Xi = 0 if the chip is non-defective and Xi =...
(a) n = 50, p = 0.095 (b) n = 100, p= 0.095 (c) n = 500, p = 0.095 (d) n = 1000, p = 0.095 (e) Comment on the effect of sample size on the observed P-value of the test.
An inspector of flow metering devices used to administer fluid intravenously will perform a hypothesis test to determine whether the mean flow rate is different from the flow rate setting of 200...
A taxpayer disposed a part of asset for 100,000 SR in cash. The taxpayer purchased that asset for 90,000 SR 5 years ago but the market value of the complete assets was as follows: Part disposed...
A company maintains debt/equity ratio of 0.6. The flotation cost of equity is 12% and flotation cost of debt it is 6%. The firm is considering a new project which will require $5 million in external...
Flight Caf prepares in-flight meals for airlines in its kitchen located next to a local airport. The company's planning budget for July appears below: Flight Caf Planning Budget For the Month Ended...

Suppose that a Rn that L Rm, and that f: Rn Rm. Prove that

Question:

Step by Step Answer:

Let 1 and choose 0 such t...View the full answer

An Introduction to Analysis

Students also viewed these Numerical Analysis questions