sin x 2 is not uniformly continuous Since sin2 sin 2 is the product of two differentiable functions it is differentiable and so it is continuous In particular sin2 sin 2 is continuous on 0 2 0 2 Hence it is
If something is continuous but not uniformly that means that you can always find a d that works for a given e but you have to know what x they re looking at before you can determine what it is You can give them a d that works when Sequential continuity has nothing to do with this as x sin x x sin x is continuous just not uniformly so Given 0 0 consider the function s values at points of the form 2n 2 n
sin x 2 is not uniformly continuous
sin x 2 is not uniformly continuous
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Solved Prove That F x Cos x 2 Is Not Uniformly Continuous On R
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Solved Prove That F x Cos x 2 Is Not Uniformly Continuous On R
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Can someone please explain to me why sin x 2 is not uniformly continuous On what set The reason is that the function is contionuos and bounded but its derivative is Would sin x 2 be an example of a function f R R that is continuous and bounded on R but not uniformly continuous on R
Use the Nonuniform Continuity Criterion 5 4 2 to show that the following functions are not uniformly continuous on the given sets f x x2 A 0 1 g x sin 1 x B 0 1 Let Let f 3 2 rightarrow mathbb R be given by f x x 2 This function is uniformly continuous on 3 2 Solution Let varepsilon 0 First observe that for u v in 3 2
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In particular if you choose x 2n pi and y 2n pi frac delta 2 then it will follow that 2n pi frac delta 2 sin frac delta 2 Would sin x 2 be an example of a function f R R that is continuous and bounded on R but not uniformly continuous on R
Uniform continuity In Example 1 f x xsin 1 x is uniformly con tinuous on 0 1 see below whereas in Example 2 f x sin 1 x is not uniformly continuous on 0 1 Fact 1 Suppose f To prove uniform continuity we need to show that for every 0 there exists a 0 such that for all x y in x y implies sin x sin y Given two points a and b in with a
SOLVED Prove That F x 1 X Is Not Uniformly Continuous In 0
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Solved Problem 2 Using The Definition Of Uniform Chegg
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sin x 2 is not uniformly continuous - Use the Nonuniform Continuity Criterion 5 4 2 to show that the following functions are not uniformly continuous on the given sets f x x2 A 0 1 g x sin 1 x B 0 1 Let