Question

Showing monotone convergence of recursive relation with $ x_{n+1} = \sin(x_{n}) $

score 46 · Answer 1 · 2019-09-30 09:57:38

46

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Showing monotone convergence of recursive relation with $ x_{n+1} = \sin(x_{n}) $

Published on 30 Sep 2019 - 9:57

score 714 · Answer 2 · 2019-09-30 15:07:16

714

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Does a monotonically increasing function attain a maximum on a compact subset of $\mathbb{R}$? Prove that it does, or give an example against.

Published on 30 Sep 2019 - 15:07

score 24.9k · Answer 3 · 2014-04-17 18:39:09

24.9k

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How to prove $x^3$ is strictly increasing

Published on 17 Apr 2014 - 18:39

score 7k · Answer 4 · 2014-09-10 05:28:25

7k

Views

Determining whether a polynomial is monotonic on a given interval $I$

Published on 10 Sep 2014 - 5:28

score 86 · Answer 5 · 2019-10-02 18:24:44

Asserting that equation f(x) = g(x) has one (or no) solutions can we use weak monotonic properties? Or both functions shall be strictly monotonic?

score 83 · Answer 6 · 2019-10-02 19:56:59

Can non-smooth function (first derivative is not defined at some points) be monotonic (including points where first derivative does not exist)?

score 163 · Answer 7 · 2019-10-02 21:13:09

163

Views

Prove that $f(a+b)=f(a)+f(b)$

Published on 02 Oct 2019 - 21:13

score 286 · Answer 8 · 2019-10-04 07:14:03

286

Views

Mapping the interval [0,1] to [-1,1] with side conditions

Published on 04 Oct 2019 - 7:14

score 188 · Answer 9 · 2019-10-04 14:49:03

188

Views

Leading term of monotonic polynomial shape proof with theorem?

Published on 04 Oct 2019 - 14:49

score 14 · Answer 10 · 2026-03-03 10:43:10

14

Views

The Probability Density of a Function of Random Variable (where the function over the domain is not strictly monotonous)

Published on 03 Mar 2026 - 10:43

score 314 · Answer 11 · 2019-10-05 10:08:36

314

Views

limit of non-monotone functions

Published on 05 Oct 2019 - 10:08

score 166 · Answer 12 · 2019-10-07 07:04:49

166

Views

Prove that $\left ( 1+\frac{n^{\frac{1}{n}}}{n} \right )^\frac{1}{n}+\left ( 1-\frac{n^{\frac{1}{n}}}{n} \right )^\frac{1}{n}<2$

Published on 07 Oct 2019 - 7:04

score 978 · Answer 13 · 2019-10-07 22:02:05

978

Views

To use Mean Value Theorem to prove $f(x)=\tan(x)$ increases over $(-\pi/2,\pi/2)$, don't we need $f(\pm\pi/2)$? Yet these values are undefined.

Published on 07 Oct 2019 - 22:02

score 72 · Answer 14 · 2019-10-08 10:36:41

72

Views

Finding nature of composition of function based on the details of component functions

Published on 08 Oct 2019 - 10:36

score 5k · Answer 15 · 2019-10-16 01:26:28

5k

Views

Is $1/x$ strictly decreasing?

Published on 16 Oct 2019 - 1:26

List Question

Showing monotone convergence of recursive relation with $ x_{n+1} = \sin(x_{n}) $

Does a monotonically increasing function attain a maximum on a compact subset of $\mathbb{R}$? Prove that it does, or give an example against.

How to prove $x^3$ is strictly increasing

Determining whether a polynomial is monotonic on a given interval $I$

Asserting that equation f(x) = g(x) has one (or no) solutions can we use weak monotonic properties? Or both functions shall be strictly monotonic?

Can non-smooth function (first derivative is not defined at some points) be monotonic (including points where first derivative does not exist)?

Prove that $f(a+b)=f(a)+f(b)$

Mapping the interval [0,1] to [-1,1] with side conditions

Leading term of monotonic polynomial shape proof with theorem?

The Probability Density of a Function of Random Variable (where the function over the domain is not strictly monotonous)

limit of non-monotone functions

Prove that $\left ( 1+\frac{n^{\frac{1}{n}}}{n} \right )^\frac{1}{n}+\left ( 1-\frac{n^{\frac{1}{n}}}{n} \right )^\frac{1}{n}<2$

To use Mean Value Theorem to prove $f(x)=\tan(x)$ increases over $(-\pi/2,\pi/2)$, don't we need $f(\pm\pi/2)$? Yet these values are undefined.

Finding nature of composition of function based on the details of component functions

Is $1/x$ strictly decreasing?

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