Question

Is $f(x,y) = d(x,y)$ a continuous function from a Metric space $X \times X$ to $\mathbb R$?

score 942 · Answer 1 · 2026-04-05 22:35:44

942

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Is $f(x,y) = d(x,y)$ a continuous function from a Metric space $X \times X$ to $\mathbb R$?

Published on 05 Apr 2026 - 22:35

score 70 · Answer 2 · 2019-01-06 20:41:40

70

Views

An infinity of natural numbers for which a function doesn't have a limit at $\infty$

Published on 06 Jan 2019 - 20:41

score 1.3k · Answer 3 · 2026-03-26 19:25:05

1.3k

Views

Need Help : Proving polynomials are continuous, without circular reasoning

Published on 26 Mar 2026 - 19:25

score 161 · Answer 4 · 2026-03-31 10:43:26

161

Views

Continous partial derivatives $\implies$ differentiable. What about the reciprocal?

Published on 31 Mar 2026 - 10:43

score 78 · Answer 5 · 2019-01-07 19:35:15

78

Views

Show that the following function is continuous on $[0,1].$

Published on 07 Jan 2019 - 19:35

score 763 · Answer 6 · 2019-01-07 20:40:21

763

Views

Given $f$ continuous in an interval, prove that there exists x such that $f(x+1/n) = f(x)$.

Published on 07 Jan 2019 - 20:40

score 674 · Answer 7 · 2019-01-07 22:20:40

674

Views

$\lim\limits_{n\to\infty}f\left(\frac{x}{n}\right)=0$ for every $x > 0$. Prove $\lim\limits_{x \to 0}f(x)=0$

Published on 07 Jan 2019 - 22:20

score 3.9k · Answer 8 · 2026-04-07 16:31:04

3.9k

Views

Can a cube of discontinuous function be continuous?

Published on 07 Apr 2026 - 16:31

score 43 · Answer 9 · 2019-01-08 10:58:48

43

Views

Continuity, differentiability of $f(x,y)=\frac{x^{\frac{3}{2}}y^b}{x^2+y^2}$ , $x^2+y^2\ne 0 $

Published on 08 Jan 2019 - 10:58

score 2.3k · Answer 10 · 2026-03-27 02:59:45

2.3k

Views

How to prove that $\sqrt x$ is continuous in $[0,\infty)$?

Published on 27 Mar 2026 - 2:59

score 37 · Answer 11 · 2026-02-23 04:56:27

37

Views

Deriving an inequality for a set of functions that have equi-Lipschitz first derivatives.

Published on 23 Feb 2026 - 4:56

score 59 · Answer 12 · 2019-01-08 17:58:47

59

Views

Continuous Functions and Integrability

Published on 08 Jan 2019 - 17:58

score 47 · Answer 13 · 2026-03-30 09:00:39

47

Views

Prove that $f_n$ with $f_n :[0,a]\rightarrow\mathbb{R},a\in \mathbb{R}, f_n(x)=x^n$ is continous $\forall n \in \mathbb{N}$

Published on 30 Mar 2026 - 9:00

score 291 · Answer 14 · 2019-01-08 21:59:43

Let $f:[a,b]\rightarrow\mathbb{R}$ be continuous. Prove that there exists a point $c\in[a,b]$ such that: $f(c)\leq\frac{f(a)+f(b)}{2}$

score 444 · Answer 15 · 2019-01-09 02:54:27

Consider the function $ \int_0^x [t]dt $ where $ x>0 $ and [t] denotes largest integer less than or equal to t. What is the nature of the function?

List Question

Is $f(x,y) = d(x,y)$ a continuous function from a Metric space $X \times X$ to $\mathbb R$?

An infinity of natural numbers for which a function doesn't have a limit at $\infty$

Need Help : Proving polynomials are continuous, without circular reasoning

Continous partial derivatives $\implies$ differentiable. What about the reciprocal?

Show that the following function is continuous on $[0,1].$

Given $f$ continuous in an interval, prove that there exists x such that $f(x+1/n) = f(x)$.

$\lim\limits_{n\to\infty}f\left(\frac{x}{n}\right)=0$ for every $x > 0$. Prove $\lim\limits_{x \to 0}f(x)=0$

Can a cube of discontinuous function be continuous?

Continuity, differentiability of $f(x,y)=\frac{x^{\frac{3}{2}}y^b}{x^2+y^2}$ , $x^2+y^2\ne 0 $

How to prove that $\sqrt x$ is continuous in $[0,\infty)$?

Deriving an inequality for a set of functions that have equi-Lipschitz first derivatives.

Continuous Functions and Integrability

Prove that $f_n$ with $f_n :[0,a]\rightarrow\mathbb{R},a\in \mathbb{R}, f_n(x)=x^n$ is continous $\forall n \in \mathbb{N}$

Let $f:[a,b]\rightarrow\mathbb{R}$ be continuous. Prove that there exists a point $c\in[a,b]$ such that: $f(c)\leq\frac{f(a)+f(b)}{2}$

Consider the function $ \int_0^x [t]dt $ where $ x>0 $ and [t] denotes largest integer less than or equal to t. What is the nature of the function?

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