Question

Suppose $f(x)=\frac 1t\int_0^t(f(x+y)-f(y))dy$ for all $x\in\Bbb R$ and all $t>0.$ Then show that $\exists c$ such that $f(x)=cx$ for all $x$

score 49 · Answer 1 · 2026-04-16 08:27:39

Suppose $f(x)=\frac 1t\int_0^t(f(x+y)-f(y))dy$ for all $x\in\Bbb R$ and all $t>0.$ Then show that $\exists c$ such that $f(x)=cx$ for all $x$

score 71 · Answer 2 · 2026-04-17 11:58:38

71

Views

Evaluate $\int_{S}\frac{z}{(x^2+y^2+z^2)^{3/2}}dV$, where $S$ is the region between $x^2+y^2+z^2=2z$ and $x^2+y^2+z^2=1$

Published on 17 Apr 2026 - 11:58

score 37 · Answer 3 · 2026-04-12 07:33:02

37

Views

The Countable Collection of Measures on a Given Measurable Space Is a Convex Cone

Published on 12 Apr 2026 - 7:33

score 50 · Answer 4 · 2026-04-16 05:39:10

50

Views

Prove that $ \lambda \in \mathbb{C} \land \lambda^2 = Re(\lambda) \Rightarrow \lambda \in \mathbb{R} $

Published on 16 Apr 2026 - 5:39

score 117 · Answer 5 · 2026-04-15 22:34:57

117

Views

Brezis' exercise 4.14: Egorov theorem

Published on 15 Apr 2026 - 22:34

score 63 · Answer 6 · 2026-04-14 07:58:00

63

Views

$\varphi(an+b)<kn$ for infinitely many n

Published on 14 Apr 2026 - 7:58

score 108 · Answer 7 · 2026-04-13 13:15:43

108

Views

Exercise 10, Section 1.3 of Hungerford’s Abstract Algebra

Published on 13 Apr 2026 - 13:15

score 298 · Answer 8 · 2026-04-16 05:38:35

298

Views

Find the point on the line $6x+5y+3=0$ which is closest to the point $(5,5)$

Published on 16 Apr 2026 - 5:38

score 48 · Answer 9 · 2026-04-11 23:26:38

48

Views

Fourier Series coefficients of the derivative

Published on 11 Apr 2026 - 23:26

score 124 · Answer 10 · 2026-03-26 19:19:01

124

Views

Given $m$ objects of type A and $n$ objects of type B, arrange them such that there are not more than two consecutive objects of type B.

Published on 26 Mar 2026 - 19:19

score 149 · Answer 11 · 2026-05-04 19:16:46

149

Views

Postnikov towers are unique up to homotopy

Published on 04 May 2026 - 19:16

score 159 · Answer 12 · 2026-04-11 08:37:40

159

Views

An exercise from Serre characterizing doubly transitive groups

Published on 11 Apr 2026 - 8:37

score 1.1k · Answer 13 · 2026-04-17 11:11:14

1.1k

Views

Solve the following differential equation : $\frac{d^3y}{dx^3}+y=3+e^{-x}+5e^{2x}.$

Published on 17 Apr 2026 - 11:11

score 55 · Answer 14 · 2026-04-13 11:53:14

55

Views

Proving a set is compact and using density to show that something is not a homeomorphism

Published on 13 Apr 2026 - 11:53

score 45 · Answer 15 · 2026-04-16 06:21:40

45

Views

verification of proof for uniform continuity for a function $f: \mathbb{R}^2 \rightarrow \mathbb{R}$, defined by $f(x,y) = 2x$ in a metric space

Published on 16 Apr 2026 - 6:21

List Question

Suppose $f(x)=\frac 1t\int_0^t(f(x+y)-f(y))dy$ for all $x\in\Bbb R$ and all $t>0.$ Then show that $\exists c$ such that $f(x)=cx$ for all $x$

Evaluate $\int_{S}\frac{z}{(x^2+y^2+z^2)^{3/2}}dV$, where $S$ is the region between $x^2+y^2+z^2=2z$ and $x^2+y^2+z^2=1$

The Countable Collection of Measures on a Given Measurable Space Is a Convex Cone

Prove that $ \lambda \in \mathbb{C} \land \lambda^2 = Re(\lambda) \Rightarrow \lambda \in \mathbb{R} $

Brezis' exercise 4.14: Egorov theorem

$\varphi(an+b)<kn$ for infinitely many n

Exercise 10, Section 1.3 of Hungerford’s Abstract Algebra

Find the point on the line $6x+5y+3=0$ which is closest to the point $(5,5)$

Fourier Series coefficients of the derivative

Given $m$ objects of type A and $n$ objects of type B, arrange them such that there are not more than two consecutive objects of type B.

Postnikov towers are unique up to homotopy

An exercise from Serre characterizing doubly transitive groups

Solve the following differential equation : $\frac{d^3y}{dx^3}+y=3+e^{-x}+5e^{2x}.$

Proving a set is compact and using density to show that something is not a homeomorphism

verification of proof for uniform continuity for a function $f: \mathbb{R}^2 \rightarrow \mathbb{R}$, defined by $f(x,y) = 2x$ in a metric space

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