Question

Show that $x_{n+1} = \frac{2+x_n^2}{2x_n}$ is a decreasing sequence.

score 577 · Answer 1 · 2026-04-16 05:11:42

577

Views

Show that $x_{n+1} = \frac{2+x_n^2}{2x_n}$ is a decreasing sequence.

Published on 16 Apr 2026 - 5:11

score 72 · Answer 2 · 2026-04-17 12:39:47

72

Views

Verify proofs related to monotonicity of $x_{n+1} = {1\over 2}(x_n+y_n)$ and $y_{n+1} = \sqrt{{1\over 2}(x_n^2 + y_n^2)}$

Published on 17 Apr 2026 - 12:39

score 940 · Answer 3 · 2026-04-07 16:08:05

940

Views

Proof of Froda's Theorem (explanation)

Published on 07 Apr 2026 - 16:08

score 66 · Answer 4 · 2026-04-17 05:24:39

66

Views

Prove that $C_{3 \over 2}^n$ is bounded given $C_{a}^n = \frac{a(a-1)(a-2)\dots(a-n+1)}{n!}$

Published on 17 Apr 2026 - 5:24

score 148 · Answer 5 · 2026-04-12 23:29:15

148

Views

An Example of a Non-continuous Injection on a Real Interval, that is Not Strictly Monotonic.

Published on 12 Apr 2026 - 23:29

score 797 · Answer 6 · 2026-04-15 22:01:51

797

Views

Any countable set of real numbers is set of discontinuities of some monotone function.

Published on 15 Apr 2026 - 22:01

score 67 · Answer 7 · 2026-04-15 20:16:41

67

Views

Prove or disprove: If $f$ is increasing and differentiable on $(a,b)$ then $f'(x)\ge 0$ on $(a,b)$

Published on 15 Apr 2026 - 20:16

score 2.1k · Answer 8 · 2026-04-17 13:32:22

2.1k

Views

Are all linear functions monotonic?

Published on 17 Apr 2026 - 13:32

score 76 · Answer 9 · 2026-04-17 02:26:09

76

Views

Is the function $f(x)=\frac{\sin(\sin{(x)}+x)}{2+\cos{(\lvert x\rvert}+\cos{(x)})}$ monotonic and/or periodic?

Published on 17 Apr 2026 - 2:26

score 171 · Answer 10 · 2026-04-11 11:16:09

171

Views

Prove $f_n \to f$ uniformly on $\mathbb{R}$

Published on 11 Apr 2026 - 11:16

score 1.5k · Answer 11 · 2026-04-15 23:19:50

1.5k

Views

Prove $a_n = \sqrt{n+1}-\sqrt{n}$ is monotone $n \ge 0$.

Published on 15 Apr 2026 - 23:19

score 135 · Answer 12 · 2026-04-16 03:10:21

135

Views

Monotonicity of function $f(x)=(1+\frac1x)^x(1+x)^\frac1x$

Published on 16 Apr 2026 - 3:10

score 3.7k · Answer 13 · 2026-04-14 22:47:30

3.7k

Views

Prove inverse of strictly monotone increasing function is continuous over the range of original function

Published on 14 Apr 2026 - 22:47

score 80 · Answer 14 · 2026-04-14 02:00:43

80

Views

How to find CDF of $Y=|X|\wedge 2$ with $X\sim Laplace(\lambda)$

Published on 14 Apr 2026 - 2:00

score 144 · Answer 15 · 2026-04-14 00:59:33

144

Views

Monotonicity of tangent

Published on 14 Apr 2026 - 0:59

List Question

Show that $x_{n+1} = \frac{2+x_n^2}{2x_n}$ is a decreasing sequence.

Verify proofs related to monotonicity of $x_{n+1} = {1\over 2}(x_n+y_n)$ and $y_{n+1} = \sqrt{{1\over 2}(x_n^2 + y_n^2)}$

Proof of Froda's Theorem (explanation)

Prove that $C_{3 \over 2}^n$ is bounded given $C_{a}^n = \frac{a(a-1)(a-2)\dots(a-n+1)}{n!}$

An Example of a Non-continuous Injection on a Real Interval, that is Not Strictly Monotonic.

Any countable set of real numbers is set of discontinuities of some monotone function.

Prove or disprove: If $f$ is increasing and differentiable on $(a,b)$ then $f'(x)\ge 0$ on $(a,b)$

Are all linear functions monotonic?

Is the function $f(x)=\frac{\sin(\sin{(x)}+x)}{2+\cos{(\lvert x\rvert}+\cos{(x)})}$ monotonic and/or periodic?

Prove $f_n \to f$ uniformly on $\mathbb{R}$

Prove $a_n = \sqrt{n+1}-\sqrt{n}$ is monotone $n \ge 0$.

Monotonicity of function $f(x)=(1+\frac1x)^x(1+x)^\frac1x$

Prove inverse of strictly monotone increasing function is continuous over the range of original function

How to find CDF of $Y=|X|\wedge 2$ with $X\sim Laplace(\lambda)$

Monotonicity of tangent

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