Question: Show that the function f(x):= 1/x2 is uniformly continuous on A: = (1, ), but that it is not uniformly continuous on B: = (0,

Show that the function f(x):= 1/x2 is uniformly continuous on A: = (1, ∞), but that it is not uniformly continuous on B: = (0, ∞).

Step by Step Solution

★★★★★

3.45 Rating (171 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

If x u 1 then 1x 2 1u 2 1x 2 u 1xu 2 x u 2x ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

829-C-F-M (393).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

Q:

(a) Show that the function f (x) = In (x + x2 + 1 is an odd function. (b) Find the inverse function of f.

Q:

Show that the function f (x) = |x| from the set of real numbers to the set of nonnegative real numbers is not invertible, but if the domain is restricted to the set of nonnegative real numbers, the...

Q:

Show that the function f (x) = ax + b from R to R is invertible, where a and b are constants, with a 0, and find the inverse of f.

Q:

Could someone please check this work and let me know if it's correct and also answer the circled questions Show That f ( x ) is not uniformly continuous on ( 0, 2 ) using E and S. 2. f (z) = - on (0,...

Q:

This is real analysis. Exercise 3.4.7: Let f: (0, 1) - R be a bounded continuous function. Show that the function g(x) := x(1 -x)f(x) is uniformly continuous. Exercise 3.4.8: Show that f: (0, co) - R...

Q:

Economics questions; (1) Consider the following system of linear equations, c + 3y + 2= =1 3r + y + 22 =b cty taz =2b where a, be R are parameters. (a) Classify the system according to the values of...

Q:

29. As Liu Wen from Hebei University of Technology in Tianjin, China, has noted in the April 2001 issue of The American Mathematical Monthly, in some reputable probability and statistics texts it has...

Q:

[2) Given the matrix A = 1 3 [a) Find the characteristic polynomial and check that the eigenvalues are A, = 1 y X, = 2. )which one of them has multiplicity? (b) Determine the corresponding diagonal...

Q:

Suppose that X is a separable metric space which satisfies the Bolzano-Weierstrass Property, that Y is a complete metric space, and that E is a bounded subset of X. Prove that a function f: E Y is...

Q:

06:09 4 0 NOV EXAM 2022.pdf . . . the series _ (1 + -) [5] 1=1 (3.4) Use the Ratio Test to determine the convergence or divergence of the series } (3n)! [5] n=1 (n!)3 1 (3.5) Use the Integral Test to...

Q:

Discuss the concept of the Process Spectrum. Use examples where appropriate.

Q:

How do the five dimensions of service quality differ from those of product quality?

Q:

Q: Required: Select the managerial accounting objective ( s ) that are applicable for each scenario: planning, controlling ( including performance evaluation ) , or making decisions. Each of the...

Q:

List the objectives of advertising.

Q:

Use the Internet Use by World Regions table for Exercises 31 and 32. 1. Find the increase in Internet users in Europe from 2008 to 2013. 2. Find the difference in the number of Internet users in 2013...

Q:

The following bar graph shows the monthly savings account balances for a freshman attending a local community college. Use this graph to answer Exercises 33 through 36. 1. During what month was the...

Q:

Round to the given place. 1. 43 to the nearest ten 2. 45 to the nearest ten 3. 876 to the nearest ten 4. 493 to the nearest hundred 5. 3829 to the nearest hundred

Q:

A major daily newspaper charges $ 4 0 0 ( paid in advance ) for an annual subscription, or $ 4 1 per month payable at the end of each month to the carrier. What is the effective interest rate being...

Q:

is 3.12 lbs. 2. An attitude survey of an ER shows 85% overall satisfaction with the care provided

Q:

At December 3 1 , 2 0 2 1 , Splish Company had a credit balance of $ 1 9 , 1 0 0 in Allowance for Doubtful Accounts. During 2 0 2 2 . Splish wrote off accounts totaling $ 1 1 , 1 0 0 . One of those...