Prove that if f: Rn Rm is differentiable at a Rn, then it is continuous at

Question:

Prove that if f: Rn → Rm is differentiable at a € Rn, then it is continuous at a.

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: Sep 30, 2009 04:39 AM

See More Questions

Prove that if f and g are integrable on [a, b], then so are f g and f g (see Exercise 3.1.8).
Prove that if f is integrable on [0,1] and > 0, then for all a 1/n lim
Prove that if f is absolutely integrable on (l, ), then lime, f(x" ) dx=0.
What type of isomers are exhibited by [Fe(en) 3 ]Cl 2 (en = ethane-1,2-diamine)? no isomers are possible. cis and trans isomers fac and mer isomers optical isomers
You need to write a paper about LinkedIn, The term paper assignment directly relates "Assess the distinctive HR practices of employers-of-choice and compare and contrast HR policies and practices...
If A, B, and C are mutually exclusive events with P(A) = 0.2, P (B) =0.3, and P(C) = 0.4, determine the following probabilities: (a) P (A U B U C) (b) P (A B C) (c) P (A B) (d) P [(A U B) C] (e) P (A...
(p. 548). Recall that four different exposure times were studied8, 10, 12, and 14 minutesand that the measure of print quality used was dot area (hundreds of dots per square millimeter). Tukeys...
As a jewelry store manager, you want to offer credit, with interest on outstanding balances paid monthly. To carry receivables, you must borrow funds from your bank at a nominal 6%, monthly...
For Ying's thre Ying maximizes utility by setting the marginal benefit from working on the project, which is 8 (hx + hy) - 0.5, equal to the marginal cost, which is 1, and then solving for hy: 8 (hx...
In 2016, Food Dive reported that packaged food manufacturers were seeing sales decline as consumers turned away from foods like mass-produced soda and cereal. Responding to declining sales and rising...
Suppose a static factor of safety is defined as the ratio of resisting to driving forces, that is, FS = R/D. Show that a factor of safety less than one implies acceleration is impending
A function f: R2 R is said to be independent of the second variable if for each x R we have f (x, y1) = f (x, y2) for all y1, y2. R Show that f is independent of the second variable if and only if...
The Committee of Sponsoring Organizations of the Treadway Commission has discussed in its document entitled COSO ERM Framework (2004), a comprehensive approach to Enterprise Risk Management. Discuss...
Verify that the following general thermodynamic property relationships are valid for the specific case of an ideal gas: (a) T = au (b) P = -9) av
Performance management systems that do not make true contribution to the organizational goals are not true performance management systems. List and describe at least five contributions a good...
How do cognitive biases, such as confirmation bias and anchoring, influence strategic decision-making processes at the executive level, and what measures can be implemented to mitigate their impact ?
How do multi-track diplomacy frameworks, integrating official, unofficial, and grassroots efforts at different levels of society, enhance the effectiveness and inclusivity of conflict resolution...
As explained by Welch, what should managers do to determine what their own organizations have been up to ?
Explain how exchange rates are determined. L01
Why is a help desk and production support critical to system implementations? Discuss its interrelationship with the problem management and reporting system.
The acronym KPI relates to which of the following phrases? a. Key Profitability Indicator. b. Key Performance Indicator. c. Known Performance Increment. d. Known Profitability Increment.
Question 7 of 7 0/14 W PIERDERY Current Attempt in Progress Your answer is incorrect Buffalo Corporation adopted the dollar value LIFO retail inventory method on January 1, 2019. At that time the...
Cost of debt with fees . Kenny Enterprises will issue a bond with a par value of $1,000, a maturity of twenty years, and a coupon rate of 9.9% with semiannual payments, and will use an investment...
Assume that an investment of $100,000 is expected to grow during the next year by 8% with SD 20%, and that the return is normally distributed. Whats the 5% VaR for the investment? A. $24,898 B....

Prove that if f: Rn Rm is differentiable at a Rn, then it is continuous at

Question:

Step by Step Answer:

If is different...View the full answer

An Introduction to Analysis

Students also viewed these Basic questions