Question

What is the radius of smallest circular disk large enough to cover every acute isosceles triangle of a given perimeter $L$?

score 1.8k · Answer 1 · 2015-08-26 09:31:24

1.8k

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What is the radius of smallest circular disk large enough to cover every acute isosceles triangle of a given perimeter $L$?

Published on 26 Aug 2015 - 9:31

score 242 · Answer 2 · 2015-08-26 11:11:49

Show that for each $a>0$ the function $e^{-ax}x^{a^2}$ has a maximum value, say $F(a)$, and that $F(x)$ has a minimum value $e^{-e/2}$

score 5.5k · Answer 3 · 2015-08-26 13:46:32

5.5k

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Prove that the least intercept made on the tangents to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ by the axes is $a+b$.

Published on 26 Aug 2015 - 13:46

score 323 · Answer 4 · 2015-08-26 16:09:19

323

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Prove that if $\lim_{n\to \infty} a_n=l$ then $\lim \sup a_n=\lim \inf a_n=l$

Published on 26 Aug 2015 - 16:09

score 470 · Answer 5 · 2026-04-02 13:58:04

470

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Wheeden-Zygmund exercise

Published on 02 Apr 2026 - 13:58

score 74 · Answer 6 · 2026-04-02 14:00:57

74

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Prove the following properties of sequence

Published on 02 Apr 2026 - 14:00

score 60 · Answer 7 · 2015-08-28 20:06:28

60

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Limit of the recurrence $b_{n+1}=\sqrt{2+b_n}$ with $b_1=\sqrt{2}$.

Published on 28 Aug 2015 - 20:06

score 75 · Answer 8 · 2015-08-28 22:07:13

75

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Every closed subset of $\mathbb R^n$ has a point that minimizes the distance to a given point $p\in\mathbb R^n$

Published on 28 Aug 2015 - 22:07

score 168 · Answer 9 · 2015-08-29 14:01:19

168

Views

Proving a formula about the supremum of a finite family of sets by induction

Published on 29 Aug 2015 - 14:01

score 67 · Answer 10 · 2015-08-29 16:26:04

67

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Infimum of $f(x): (0,\infty) \to \mathbb R$, $f(x) = \ln(e^x-1)+\frac2x-x$

Published on 29 Aug 2015 - 16:26

score 1k · Answer 11 · 2015-08-30 23:27:11

1k

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If an element $a \in A$ is an upper bound for $A$, then $a = \sup A$.

Published on 30 Aug 2015 - 23:27

score 57 · Answer 12 · 2015-08-31 17:44:05

57

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Query about non-singular transformation of vectors

Published on 31 Aug 2015 - 17:44

score 439 · Answer 13 · 2015-09-01 01:02:48

439

Views

Partial ordered sets and supremum.

Published on 01 Sep 2015 - 1:02

score 199 · Answer 14 · 2015-09-03 07:45:30

199

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On the integration of a Lebesgue measurable function

Published on 03 Sep 2015 - 7:45

score 189 · Answer 15 · 2015-09-05 18:59:53

189

Views

A Proof for a Sequence Convergence

Published on 05 Sep 2015 - 18:59

List Question

What is the radius of smallest circular disk large enough to cover every acute isosceles triangle of a given perimeter $L$?

Show that for each $a>0$ the function $e^{-ax}x^{a^2}$ has a maximum value, say $F(a)$, and that $F(x)$ has a minimum value $e^{-e/2}$

Prove that the least intercept made on the tangents to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ by the axes is $a+b$.

Prove that if $\lim_{n\to \infty} a_n=l$ then $\lim \sup a_n=\lim \inf a_n=l$

Wheeden-Zygmund exercise

Prove the following properties of sequence

Limit of the recurrence $b_{n+1}=\sqrt{2+b_n}$ with $b_1=\sqrt{2}$.

Every closed subset of $\mathbb R^n$ has a point that minimizes the distance to a given point $p\in\mathbb R^n$

Proving a formula about the supremum of a finite family of sets by induction

Infimum of $f(x): (0,\infty) \to \mathbb R$, $f(x) = \ln(e^x-1)+\frac2x-x$

If an element $a \in A$ is an upper bound for $A$, then $a = \sup A$.

Query about non-singular transformation of vectors

Partial ordered sets and supremum.

On the integration of a Lebesgue measurable function

A Proof for a Sequence Convergence

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