List questions from continuity

Published on 24 Mar 2018 - 17:45

34

Views

Show that $f_n(t) = n\int_{t-1/n}^t1_{\{|f(s\vee 0)|\le n\}}f(s\vee 0)\,ds \rightarrow f(t)$

Published on 29 Mar 2026 - 20:06

392

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Delta Epsilon Proof for Ratio of Polynomials

Published on 25 Mar 2026 - 3:19

46

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Ways to see the result of $\lim_{z\to 0}f(z)$

Published on 25 Mar 2018 - 16:47

56

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Is the following definition of continuity accurate?

Published on 25 Mar 2026 - 17:53

259

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Sufficient conditions for when continuity at a point implies continuity in a neighbourhood of that point

Published on 26 Mar 2018 - 14:44

110

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Proving that continuous function $f:[0,2] \to \mathbb{R}$ such as $f(0)=f(2)$, $\exists x \in [0,1]:f(x)=f(x+1)$

Published on 25 Mar 2026 - 17:21

47

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Continuous uniform distribution question

Published on 25 Mar 2026 - 9:33

63

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Continuous function show a bound on the image gives a closed preimage

Published on 26 Mar 2018 - 23:00

44

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Proving or Disproving: Proximal mapping of f = gradient of g

Published on 25 Mar 2026 - 16:03

47

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Logic for If and only if proof

Published on 27 Mar 2018 - 2:36

53

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$f(x)=\sin^{-1}(\sin x)$; $x$ is real then prove that $f$ is continuous for all $x$ but not differentiable for all $x =(2k+1)π/2$?

Published on 27 Mar 2018 - 5:42

389

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Continuity of rational functions between affine algebraic sets

Published on 25 Mar 2026 - 6:10

87

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A special restriction of a non-constant continuous function

Published on 25 Mar 2026 - 18:14

78

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Prove that $\lim_{x \to 2} x^2 = 4$.

Published on 27 Mar 2018 - 9:40

List Question

How do I tell if a function is continuous?

Show that $f_n(t) = n\int_{t-1/n}^t1_{\{|f(s\vee 0)|\le n\}}f(s\vee 0)\,ds \rightarrow f(t)$

Delta Epsilon Proof for Ratio of Polynomials

Ways to see the result of $\lim_{z\to 0}f(z)$

Is the following definition of continuity accurate?

Sufficient conditions for when continuity at a point implies continuity in a neighbourhood of that point

Proving that continuous function $f:[0,2] \to \mathbb{R}$ such as $f(0)=f(2)$, $\exists x \in [0,1]:f(x)=f(x+1)$

Continuous uniform distribution question

Continuous function show a bound on the image gives a closed preimage

Proving or Disproving: Proximal mapping of f = gradient of g

Logic for If and only if proof

$f(x)=\sin^{-1}(\sin x)$; $x$ is real then prove that $f$ is continuous for all $x$ but not differentiable for all $x =(2k+1)π/2$?

Continuity of rational functions between affine algebraic sets

A special restriction of a non-constant continuous function

Prove that $\lim_{x \to 2} x^2 = 4$.

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