Question

Showing there exists $\zeta$ such that $f(\zeta)=f'(\zeta)$ by Rolle's theorem: motivating the definition of an auxiliary function

score 145 · Answer 1 · 2026-04-14 05:55:28

145

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Showing there exists $\zeta$ such that $f(\zeta)=f'(\zeta)$ by Rolle's theorem: motivating the definition of an auxiliary function

Published on 14 Apr 2026 - 5:55

score 61 · Answer 2 · 2026-04-15 14:37:24

61

Views

Series' rearrangements and colourings

Published on 15 Apr 2026 - 14:37

score 204 · Answer 3 · 2026-04-25 10:38:35

204

Views

Squaring $\sqrt{(x-2)^{2}+(y-3)^{2}}=\frac{|5x+6y+5|}{\sqrt{5^{2}+6^{2}}}$ does not lose information?

Published on 25 Apr 2026 - 10:38

score 117 · Answer 4 · 2026-04-15 03:59:20

117

Views

If $f:\mathbb{R}\to\mathbb{R}$ is a differentiable function with $x^2f'(x)\to 0$ as $x\to\infty,$ then does $f(x)\to c\in\mathbb{R}$ as $x\to\infty$?

Published on 15 Apr 2026 - 3:59

score 46 · Answer 5 · 2026-04-16 04:57:20

46

Views

Where do I find examples or problems that illustrate doing proofs backward?

Published on 16 Apr 2026 - 4:57

score 55 · Answer 6 · 2026-04-13 00:57:33

55

Views

Show that the function converges to the following limit.

Published on 13 Apr 2026 - 0:57

score 167 · Answer 7 · 2026-04-16 05:23:20

167

Views

If dividing by a variable gives a contradiction, does that imply that the variable must be zero?

Published on 16 Apr 2026 - 5:23

score 60 · Answer 8 · 2026-04-12 05:51:44

60

Views

Help With Atypical Induction Proof

Published on 12 Apr 2026 - 5:51

score 146 · Answer 9 · 2026-04-16 08:43:00

146

Views

Prove that the probability of a knight to get in a specific square is 1.

Published on 16 Apr 2026 - 8:43

score 556 · Answer 10 · 2026-04-10 03:46:28

556

Views

How should an advanced undergraduate improve olympiad-style problem solving?

Published on 10 Apr 2026 - 3:46

score 136 · Answer 11 · 2026-04-09 13:32:20

136

Views

Need analytical solution to this ODE

Published on 09 Apr 2026 - 13:32

score 61 · Answer 12 · 2026-04-16 20:33:22

61

Views

Least $k$ such that $x_1<x_2<x_3<x_4\implies (x_2-x_1)^2 + (x_3-x_2)^2 + (x_4-x_3)^2 + (x_4-x_1)^2 < k\left[ (x_3-x_1)^2 + (x_4-x_2)^2 \right]$

Published on 16 Apr 2026 - 20:33

score 44 · Answer 13 · 2026-04-15 10:16:29

44

Views

Confused about the values shown in circles (Brilliant.org)

Published on 15 Apr 2026 - 10:16

score 64 · Answer 14 · 2026-04-13 15:27:38

64

Views

Method request: Can this equation be solved?

Published on 13 Apr 2026 - 15:27

score 56 · Answer 15 · 2026-04-11 22:01:25

56

Views

Method to solve this PDE?

Published on 11 Apr 2026 - 22:01

List Question

Showing there exists $\zeta$ such that $f(\zeta)=f'(\zeta)$ by Rolle's theorem: motivating the definition of an auxiliary function

Series' rearrangements and colourings

Squaring $\sqrt{(x-2)^{2}+(y-3)^{2}}=\frac{|5x+6y+5|}{\sqrt{5^{2}+6^{2}}}$ does not lose information?

If $f:\mathbb{R}\to\mathbb{R}$ is a differentiable function with $x^2f'(x)\to 0$ as $x\to\infty,$ then does $f(x)\to c\in\mathbb{R}$ as $x\to\infty$?

Where do I find examples or problems that illustrate doing proofs backward?

Show that the function converges to the following limit.

If dividing by a variable gives a contradiction, does that imply that the variable must be zero?

Help With Atypical Induction Proof

Prove that the probability of a knight to get in a specific square is 1.

How should an advanced undergraduate improve olympiad-style problem solving?

Need analytical solution to this ODE

Least $k$ such that $x_1<x_2<x_3<x_4\implies (x_2-x_1)^2 + (x_3-x_2)^2 + (x_4-x_3)^2 + (x_4-x_1)^2 < k\left[ (x_3-x_1)^2 + (x_4-x_2)^2 \right]$

Confused about the values shown in circles (Brilliant.org)

Method request: Can this equation be solved?

Method to solve this PDE?

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