Question

Prove the equation $\ln(x) = \frac1 {x-1}$ has exactly 2 real solutions.

score 1.4k · Answer 1 · 2026-04-15 12:38:20

1.4k

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Prove the equation $\ln(x) = \frac1 {x-1}$ has exactly 2 real solutions.

Published on 15 Apr 2026 - 12:38

score 73 · Answer 2 · 2026-04-13 00:41:23

73

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Question on suprema of a set $X$ which is a subset of set of real numbers

Published on 13 Apr 2026 - 0:41

score 181 · Answer 3 · 2026-04-14 18:40:49

181

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Proof explanation to see that subset of $\mathbb{R}^2$ is not path connected.

Published on 14 Apr 2026 - 18:40

score 90 · Answer 4 · 2026-04-15 22:58:53

90

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Why is the set ${\{1\}}$ closed on $\mathbb{R}$ with the metric $d(x,y) = |x−y|$

Published on 15 Apr 2026 - 22:58

score 52 · Answer 5 · 2026-04-17 02:37:57

52

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Period $2$ solutions of $N_{t+1}=rN_t(1-N_t)$

Published on 17 Apr 2026 - 2:37

score 51 · Answer 6 · 2026-04-15 15:25:45

51

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Question about the average value of a function on the ball of radius r centered at x

Published on 15 Apr 2026 - 15:25

score 144 · Answer 7 · 2026-04-17 03:25:44

144

Views

Relation between (non-random) Big O and probability little o

Published on 17 Apr 2026 - 3:25

score 132 · Answer 8 · 2026-04-15 19:43:41

132

Views

$|a-b| \geq | |a| - |b| | \Longleftrightarrow |a-b| \geq |a| - |b| $?

Published on 15 Apr 2026 - 19:43

score 72 · Answer 9 · 2026-04-14 02:38:22

72

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Question about the Lebesgue set Lf

Published on 14 Apr 2026 - 2:38

score 2.3k · Answer 10 · 2026-04-14 20:19:28

2.3k

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Is possible to use "Feynman's trick" (differentiate under the integral or Leibniz integral rule) to calculate $\int_0^1 \frac{\ln(1-x)}{x}dx\:?$

Published on 14 Apr 2026 - 20:19

score 270 · Answer 11 · 2026-04-11 01:28:54

270

Views

Computing Partial Derivatives using implicit function theorem

Published on 11 Apr 2026 - 1:28

score 71 · Answer 12 · 2026-04-11 01:28:47

71

Views

How can I prove that the following function is increasing in x?

Published on 11 Apr 2026 - 1:28

score 2.4k · Answer 13 · 2026-04-15 13:52:09

2.4k

Views

Why does $f(x)=x$ not have a maximum on open interval $(0,1)$?

Published on 15 Apr 2026 - 13:52

score 63 · Answer 14 · 2026-04-17 05:23:11

63

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Prove $\lim_{N\to\infty} \int_{a}^{b} f_N (x) dx = \int_{a}^{b} \lim_{N\to\infty} f_N(x) dx$

Published on 17 Apr 2026 - 5:23

score 41 · Answer 15 · 2026-04-15 00:35:27

41

Views

plot the set $M:= \{z \in \mathbb{C}; Im \left( \frac{z+i}{z-2} \right) = 0\}$

Published on 15 Apr 2026 - 0:35

List Question

Prove the equation $\ln(x) = \frac1 {x-1}$ has exactly 2 real solutions.

Question on suprema of a set $X$ which is a subset of set of real numbers

Proof explanation to see that subset of $\mathbb{R}^2$ is not path connected.

Why is the set ${\{1\}}$ closed on $\mathbb{R}$ with the metric $d(x,y) = |x−y|$

Period $2$ solutions of $N_{t+1}=rN_t(1-N_t)$

Question about the average value of a function on the ball of radius r centered at x

Relation between (non-random) Big O and probability little o

$|a-b| \geq | |a| - |b| | \Longleftrightarrow |a-b| \geq |a| - |b| $?

Question about the Lebesgue set Lf

Is possible to use "Feynman's trick" (differentiate under the integral or Leibniz integral rule) to calculate $\int_0^1 \frac{\ln(1-x)}{x}dx\:?$

Computing Partial Derivatives using implicit function theorem

How can I prove that the following function is increasing in x?

Why does $f(x)=x$ not have a maximum on open interval $(0,1)$?

Prove $\lim_{N\to\infty} \int_{a}^{b} f_N (x) dx = \int_{a}^{b} \lim_{N\to\infty} f_N(x) dx$

plot the set $M:= \{z \in \mathbb{C}; Im \left( \frac{z+i}{z-2} \right) = 0\}$

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