Question

Find $\lim_{x \to -1} 1/(\sqrt{|x|-\{-x\}})$ where $\{\}$ denotes the fractional part.

score 72 · Answer 1 · 2019-01-15 13:42:24

72

Views

Find $\lim_{x \to -1} 1/(\sqrt{|x|-\{-x\}})$ where $\{\}$ denotes the fractional part.

Published on 15 Jan 2019 - 13:42

score 232 · Answer 2 · 2019-01-27 01:45:44

232

Views

$| \sin x| > \frac{\sqrt{2-\sqrt{2}}}{2}$ iff $1/8< \{ \frac{x}{\pi}\} < 7/8$ where $\{x\}$ is the fractional part of $x$

Published on 27 Jan 2019 - 1:45

score 115 · Answer 3 · 2019-02-05 17:58:06

115

Views

Trigonometric integral involving the fractional part function

Published on 05 Feb 2019 - 17:58

score 167 · Answer 4 · 2019-02-12 11:12:58

167

Views

Finding $\lim\limits_{x\to 0} \frac{\lfloor x \rfloor}{x}$ and the different definitions of fractional part function.

Published on 12 Feb 2019 - 11:12

score 431 · Answer 5 · 2019-02-14 09:18:36

431

Views

Fractional part function of $\frac{y}{n} + k$

Published on 14 Feb 2019 - 9:18

score 167 · Answer 6 · 2019-02-24 17:58:48

167

Views

Integral $\int_0^1 x^n\left\{\frac{k}{x}\right\}dx$

Published on 24 Feb 2019 - 17:58

score 131 · Answer 7 · 2019-03-09 15:36:30

131

Views

Reasoning with fractional parts and the Möbius function.

Published on 09 Mar 2019 - 15:36

score 308 · Answer 8 · 2026-03-21 16:46:36

308

Views

Doubt on Integration

Published on 21 Mar 2026 - 16:46

score 2.5k · Answer 9 · 2019-04-01 23:28:53

2.5k

Views

Calculate the difference in wavelength of the Balmer-$\alpha$ line ($n = 3$ to $n = 2$) in hydrogen and deuterium

Published on 01 Apr 2019 - 23:28

score 191 · Answer 10 · 2026-03-22 10:11:50

191

Views

Does $\sum_{k=1}^n|\cot \sqrt2\pi k|$ tends to $An\ln n$ as $n\to\infty$?

Published on 22 Mar 2026 - 10:11

score 180 · Answer 11 · 2019-04-19 20:55:22

180

Views

Counting the number of integers with their least prime factor greater than $x$ between $ax$ and $ax+x$

Published on 19 Apr 2019 - 20:55

score 34 · Answer 12 · 2019-04-21 07:37:32

34

Views

proving floor, and rounding floats in some programming languages

Published on 21 Apr 2019 - 7:37

score 86 · Answer 13 · 2019-04-21 08:17:46

86

Views

Counting integers with a least prime factor greater than $x$ in a sequence of $x$ consecutive integers.

Published on 21 Apr 2019 - 8:17

score 388 · Answer 14 · 2019-05-07 14:11:10

388

Views

Find the total number of solution of the equation

Published on 07 May 2019 - 14:11

score 71 · Answer 15 · 2019-05-19 15:25:53

71

Views

Finding the limit of this recurrence relation

Published on 19 May 2019 - 15:25

List Question

Find $\lim_{x \to -1} 1/(\sqrt{|x|-\{-x\}})$ where $\{\}$ denotes the fractional part.

$| \sin x| > \frac{\sqrt{2-\sqrt{2}}}{2}$ iff $1/8< \{ \frac{x}{\pi}\} < 7/8$ where $\{x\}$ is the fractional part of $x$

Trigonometric integral involving the fractional part function

Finding $\lim\limits_{x\to 0} \frac{\lfloor x \rfloor}{x}$ and the different definitions of fractional part function.

Fractional part function of $\frac{y}{n} + k$

Integral $\int_0^1 x^n\left\{\frac{k}{x}\right\}dx$

Reasoning with fractional parts and the Möbius function.

Doubt on Integration

Calculate the difference in wavelength of the Balmer-$\alpha$ line ($n = 3$ to $n = 2$) in hydrogen and deuterium

Does $\sum_{k=1}^n|\cot \sqrt2\pi k|$ tends to $An\ln n$ as $n\to\infty$?

Counting the number of integers with their least prime factor greater than $x$ between $ax$ and $ax+x$

proving floor, and rounding floats in some programming languages

Counting integers with a least prime factor greater than $x$ in a sequence of $x$ consecutive integers.

Find the total number of solution of the equation

Finding the limit of this recurrence relation

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