Show that the following function is continuous only at x = 0: f(x) = -x for x

Question:

Show that the following function is continuous only at x = 0:

f(x) = -x for x rational for x irrational

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

Step by Step Answer:

Related Book For answer-question

Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

See More Books

Question Posted: Nov 03, 2023 10:09 AM

See More Questions

In annual report, WRM Athletic Supply, Inc. includes the following five-year financial summary: Analyze the companys financial summary for the fiscal years 2016-2020 to decide whether to invest in...
Show that the following functions belong to R*[0, 1] by finding a function Fk that is continuous on [0, 1] and such that Fk(x) = fk(x) for x [0, 1]\Ek, for some finite set Ek. (a) f1(x) := (x + 1)/x...
Show that the following function satisfies the properties of a joint probability mass function. Determine the following: (a) P(X <2.5, Y <3) (b) P(X <2.5) (c) P(Y <3) (d) P(X >1.8, Y > 4.7) (e) E(X),...
In the OKR goal-setting framework, what is the difference between objectives and key results? Objectives deal with measurable aspects of a company's processes, while key results deal with...
Creole Industries, Inc., estimates that if it spent an additional $20,000 to hire another collection agent in its credit department, it could lower its bad-debt loss ratio to 3.5 percent from a...
Object is defined as something that is or is capable of being seen, touched or otherwise sensed and about which users store data and associate behavior. Please explain what it means by something,...
CMS is a claims processing company in Mobile, Alabama. Chastity Jones, a black woman, completed an online employment application for a customer service position with CMS. Jones interviewed with a...
The comparative statements of Villa Tool Company are presented below. All sales were on account. The allowance for doubtful accounts was $3,200 on December 31, 2011, and $3,000 on December 31, 2010....
Prove that for all x = R, if a, b = Z such that x = a + b2, then a and b are unique.
Show that is a discontinuous function for all x, where (x) is defined as follows: Show that 2 is continuous for all x. f(x) = 1 -1 for x rational for x irrational
Explain why exists but does not exist. What is lim sin X0 X
Differentiate the function. f() = ln 1/
During Pete's exit interview he states that he did not receive managerial direction or training in regard to accessing computer systems and online patient records. The hospital administrator reviews...
k=0 2k 'WI Find the sum of the series:
Using the two article links below Coca Cola and Starbucks, compare these two brands to uncover how the branding makes them part of the top 10 list of successful brands worldwide. Answer the following...
"what is the role of the government interest in determining the constitutionality of government actions? Respond with referenced to atleast 3 substantive areas of constitutional law"
Fit and Fab is a well-established CBD Gym. It currently employs; a Manager, (employed 8 years) 2 Assistant Managers, (both new) 2 Reception Staff, (employed 2 months and 2 years) 4 Full Time Personal...
On August 31, 2015, the general ledger of The Dean Acting Academy shows a balance for cash of $7,944. Cash receipts yet to be deposited into the checking account total $3,338, and checks written by...
How does health insurance risk differ from other types of insurance risk (e.g., automobile or homeowners insurance)? What is the difference between cost sharing and cost shifting? Is retiree health...
At noon, ship A is 100 km west of ship B. Ship A is sailing south at 35 km/h and ship B is sailing north at 25 km/h. How fast is the distance between the ships changing at 4:00 PM?
Water is leaking out of an inverted conical tank at a rate of 10,000 cm/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at...
A water trough is 10 m long and a cross-section has the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 80 cm wide at the top, and has height 50 cm. If the trough is being filled...
Hi Barbara, Look, we need to bring our costs down and our productivity up this quarter, and your department is one of the key areas where I'm looking to accomplish both goals. I've been noticing that...
No matter which topic you choose, nned a Routine Inquiry designed to glean information that you need via relevant, specific questions. You should include a full Memorandum heading as though you were...
The intercultural business communication process as the interaction of three variables: culture, business, and communication. Identify five sub-variables for each of these three components (culture,...

Show that the following function is continuous only at x = 0: f(x) = -x for x

Question:

f(x) = -x for x rational for x irrational

Step by Step Answer:

Let fx x for x rational and fx x for x irrational Now f0 0 since 0 is rational Moreover as x ...View the full answer

Calculus

Students also viewed these Mathematics questions