1 x 2 is not uniformly continuous

1 x 2 is not uniformly continuous Ask Question Asked 8 years 2 months ago Modified 1 year 2 months ago Viewed 4k times 1 I need to show that 1 x2 1 x 2 is not uniformly continuous on the interval 0

0 I am trying to prove the function in the title is not uniformly continuous on 0 2 Different from the proof given in proof I proceed to show the proof following Prove that each of the following functions is not uniformly continuous on the given domain f x x 2 on mathbb R f x sin frac 1 x on 0 1 f x ln x

1 x 2 is not uniformly continuous

1 x 2 is not uniformly continuous
https://i.ytimg.com/vi/U-UmtZkCHwU/maxresdefault.jpg

Solved If f x Is Uniformly Continuous And Bounded 9to5Science
https://sgp1.digitaloceanspaces.com/ffh-space-01/9to5science/uploads/post/avatar/32411/template_if-f-x-is-uniformly-continuous-and-bounded-below-1-f-is-uniformly-continuous20220620-2963525-1p8oqaf.jpg

A Continuous Function F Is Defined On The Closed Interval 4 6
https://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/discontinuous-functions-types-1-1629107462.png

Homework Help Calculus and Beyond Homework Help Show that is not uniformly continuous on 0 Terrell Jul 25 2018 Continuous Proof verification Real 2 so 0 c 2

Solution By the definition of uniform continuity for every 0 we must find a 0 such that for all x y in the domain if x y then f x f y We show that fis not uniformly continuous on S i e 9 0 8 0 9x 0 2S9x2S jx x 0j and 1 x 1 x 0 Let 1 Choose 0 Let x 0 min 1 and x x 0 2 Then jx x 0j x 0 2 2

More picture related to 1 x 2 is not uniformly continuous

Figure Below Shows A Thin Uniformly Charged Rod Of L SolvedLib
https://cdn.numerade.com/ask_images/96b3cc781f54467fa49bc8a6bb419f79.jpg

Advanced Calculus Uniform Continuity Proof F x X x 1 On 2
https://i.ytimg.com/vi/axQI2zA-r9M/maxresdefault.jpg

Solved Show That The Function F x Uniformly Continuous On Chegg
https://media.cheggcdn.com/media/0a6/0a6d8f82-dd80-46bd-8208-9225c60efa64/phpIbVNPq.png

F x sin 1 x from Example 2 is NOT uniformly continuous on 0 1 because fhas no continuous extension on a b Proof The proof is magical We ll do some wishful thinking Try to prove it Example 1 The function f x 1 1 x2 is uniformly continuous on R Proof Note that for any x u 2 R jf x 1 f u j x2 jx uj jx 1 u2 1 x2 1 u2

f x f y Alternatively you can elementarily show that f is Lipschitz on mu infty for mu 0 using the fact that lvert 1 x 1 y rvert lvert x y rvert xy 2 and xy mu 2 To show

Solved Formal Definition Of not Uniformly Continuous 9to5Science
https://sgp1.digitaloceanspaces.com/ffh-space-01/9to5science/uploads/post/avatar/48676/template_formal-definition-of-not-uniformly-continuous20220625-217520-4adaaq.jpg

Solved The Second Example Shows That non uniform Chegg
https://d2vlcm61l7u1fs.cloudfront.net/media/b4d/b4d13865-15dc-42bd-98b7-68ca15cabd06/phpkIYWxA.png

1 x 2 is not uniformly continuous - A function f x is not uniformly continuous on D if there is some 0 such that for every 0 no matter how small it is possible to nd x y 2D with jx yj but jf x f y j For