Question

Clarification regarding existence in case of Monotone Convergence Theorem

score 33 · Answer 1 · 2026-04-13 19:22:28

33

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Clarification regarding existence in case of Monotone Convergence Theorem

Published on 13 Apr 2026 - 19:22

score 123 · Answer 2 · 2026-04-14 10:34:50

123

Views

A definite integral about lacunary function.(And a calculation of a limit added.)

Published on 14 Apr 2026 - 10:34

score 3.5k · Answer 3 · 2026-04-13 17:44:38

3.5k

Views

Converse of Bolzano-Weierstrass theorem

Published on 13 Apr 2026 - 17:44

score 597 · Answer 4 · 2026-04-16 03:19:04

597

Views

On the integral $\int_0^\pi\sin(x+\sin(x+\sin(x+\cdots)))\,dx$

Published on 16 Apr 2026 - 3:19

score 103 · Answer 5 · 2026-04-17 05:37:51

103

Views

Showing the limit of $\int_x^\infty (y \log y)^{-1}dy$ is zero

Published on 17 Apr 2026 - 5:37

score 52 · Answer 6 · 2026-04-16 11:24:54

52

Views

Limit of the composition $f \circ f$

Published on 16 Apr 2026 - 11:24

score 73 · Answer 7 · 2026-05-14 13:48:22

73

Views

What is $\lim_{(x,y)\to(0,0)} \frac{\sin(x-y)}{x^3-y^3}$?

Published on 14 May 2026 - 13:48

score 78 · Answer 8 · 2026-04-14 07:12:25

78

Views

limit of f(n) / g(n) is a constant, which function is larger?

Published on 14 Apr 2026 - 7:12

score 67 · Answer 9 · 2026-04-16 14:12:07

67

Views

Evaluate $\lim\limits_{n \to \infty} n \ln\frac{a(\sqrt{n}-1)}{a(\sqrt{n}-1)+b}$

Published on 16 Apr 2026 - 14:12

score 101 · Answer 10 · 2026-04-16 23:22:55

101

Views

Evaluate $\lim\limits_{n \to \infty} n \left( c(n)\ln\frac{c(n)}{0.5} +(1- c(n))\ln\frac{1-c(n)}{0.5}\right)$

Published on 16 Apr 2026 - 23:22

score 179 · Answer 11 · 2026-04-17 07:02:05

179

Views

$\lim_{n\to \infty} \prod_{k=1}^n \left( \frac {2k}{2k-1}\right) \int_{-1}^{\infty} \frac {(\cos x)^{2n}}{2^x} dx$

Published on 17 Apr 2026 - 7:02

score 86 · Answer 12 · 2026-04-16 04:38:09

86

Views

Calculate the limit of a sequence $a_n = \frac{(1+3+5+...+(2n-1)}{(n^2+1)}$

Published on 16 Apr 2026 - 4:38

score 556 · Answer 13 · 2026-04-15 22:14:53

556

Views

On the integral $\int_0^\pi\sin(x\sin(x\sin(x\cdots)))\,dx$

Published on 15 Apr 2026 - 22:14

score 704 · Answer 14 · 2026-04-16 10:32:11

704

Views

On the integral $\int_{-\pi/2}^{\pi/2}\sin(x/\sin(x/\sin(x/\sin\cdots)))\,dx$

Published on 16 Apr 2026 - 10:32

score 155 · Answer 15 · 2026-04-16 01:35:09

155

Views

Least value of $L$ for $\sqrt{x^2+ax}-\sqrt{x^2+bx}<L$ for all $x>0$

Published on 16 Apr 2026 - 1:35

List Question

Clarification regarding existence in case of Monotone Convergence Theorem

A definite integral about lacunary function.(And a calculation of a limit added.)

Converse of Bolzano-Weierstrass theorem

On the integral $\int_0^\pi\sin(x+\sin(x+\sin(x+\cdots)))\,dx$

Showing the limit of $\int_x^\infty (y \log y)^{-1}dy$ is zero

Limit of the composition $f \circ f$

What is $\lim_{(x,y)\to(0,0)} \frac{\sin(x-y)}{x^3-y^3}$?

limit of f(n) / g(n) is a constant, which function is larger?

Evaluate $\lim\limits_{n \to \infty} n \ln\frac{a(\sqrt{n}-1)}{a(\sqrt{n}-1)+b}$

Evaluate $\lim\limits_{n \to \infty} n \left( c(n)\ln\frac{c(n)}{0.5} +(1- c(n))\ln\frac{1-c(n)}{0.5}\right)$

$\lim_{n\to \infty} \prod_{k=1}^n \left( \frac {2k}{2k-1}\right) \int_{-1}^{\infty} \frac {(\cos x)^{2n}}{2^x} dx$

Calculate the limit of a sequence $a_n = \frac{(1+3+5+...+(2n-1)}{(n^2+1)}$

On the integral $\int_0^\pi\sin(x\sin(x\sin(x\cdots)))\,dx$

On the integral $\int_{-\pi/2}^{\pi/2}\sin(x/\sin(x/\sin(x/\sin\cdots)))\,dx$

Least value of $L$ for $\sqrt{x^2+ax}-\sqrt{x^2+bx}<L$ for all $x>0$

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