Question

Why $(y-\overline y)^t[f(x)-f(\overline x)]\ge-\Vert y-\overline y\Vert\Vert f(x)-f(\overline x)\Vert$?

score 230 · Answer 1 · 2026-04-17 11:26:48

230

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Why $(y-\overline y)^t[f(x)-f(\overline x)]\ge-\Vert y-\overline y\Vert\Vert f(x)-f(\overline x)\Vert$?

Published on 17 Apr 2026 - 11:26

score 231 · Answer 2 · 2026-04-16 06:57:50

231

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Prob. 6, Exercises 8.14, in Apostol's CALCULUS Vol II: Given a scalar field differentiable at a point ...

Published on 16 Apr 2026 - 6:57

score 82 · Answer 3 · 2026-04-17 15:25:30

82

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uniform continuous function to be identically 0

Published on 17 Apr 2026 - 15:25

score 530 · Answer 4 · 2026-04-14 15:29:19

530

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Can the gradient of a non-constant scalar field be zero?

Published on 14 Apr 2026 - 15:29

score 302 · Answer 5 · 2026-04-16 10:38:27

302

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Prob. 9, Exercises 8.14, in Apostol's CALCULUS Vol II: If the derivatives of a scalar field on an open ball vanish in $n$ independent directions,

Published on 16 Apr 2026 - 10:38

score 622 · Answer 6 · 2026-04-08 21:18:07

622

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Fourier transform of distributions on the circle

Published on 08 Apr 2026 - 21:18

score 144 · Answer 7 · 2026-04-15 16:13:01

144

Views

Explicit expression for $b$ as a function of $a$ where $\log_b a = (a/b)^{1/2}$

Published on 15 Apr 2026 - 16:13

score 353 · Answer 8 · 2026-04-17 09:42:54

353

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Prob. 10, Exercises 8.14, in Apostol's CALCULUS Vol II: If the gradient of a differentiable scalar field is zero on an open ball, . . .

Published on 17 Apr 2026 - 9:42

score 86 · Answer 9 · 2026-04-23 18:14:15

86

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Is $n^p +\tan n,p>0$ always no no lower bound?

Published on 23 Apr 2026 - 18:14

score 30 · Answer 10 · 2026-04-15 08:06:03

30

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How to show that $\lim_{N\to\infty}\int_{|x|>N} |x|^3e^{-4x^2} dx=0$?

Published on 15 Apr 2026 - 8:06

score 68 · Answer 11 · 2026-04-14 23:47:12

68

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How Fourier coefficients of $\sum_{k\in \mathbb Z} g(x+ 2k\pi)$ and $\sum_{k\in \mathbb Z} g(x+ (2k+1)\pi) $ are related?

Published on 14 Apr 2026 - 23:47

score 3.5k · Answer 12 · 2026-04-11 08:05:01

3.5k

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How to prove a cone is convex and closed?

Published on 11 Apr 2026 - 8:05

score 68 · Answer 13 · 2026-04-09 01:56:25

68

Views

Complex Analysis: Transformations and Equation Solutions

Published on 09 Apr 2026 - 1:56

score 180 · Answer 14 · 2026-04-16 06:45:52

180

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How to compute $\sum_n(2n - \sqrt{n^2+1}-\sqrt{n^2-1})$?

Published on 16 Apr 2026 - 6:45

score 1.5k · Answer 15 · 2026-04-13 16:18:05

1.5k

Views

Linearization method or Lyapunov function - example

Published on 13 Apr 2026 - 16:18

List Question

Why $(y-\overline y)^t[f(x)-f(\overline x)]\ge-\Vert y-\overline y\Vert\Vert f(x)-f(\overline x)\Vert$?

Prob. 6, Exercises 8.14, in Apostol's CALCULUS Vol II: Given a scalar field differentiable at a point ...

uniform continuous function to be identically 0

Can the gradient of a non-constant scalar field be zero?

Prob. 9, Exercises 8.14, in Apostol's CALCULUS Vol II: If the derivatives of a scalar field on an open ball vanish in $n$ independent directions,

Fourier transform of distributions on the circle

Explicit expression for $b$ as a function of $a$ where $\log_b a = (a/b)^{1/2}$

Prob. 10, Exercises 8.14, in Apostol's CALCULUS Vol II: If the gradient of a differentiable scalar field is zero on an open ball, . . .

Is $n^p +\tan n,p>0$ always no no lower bound?

How to show that $\lim_{N\to\infty}\int_{|x|>N} |x|^3e^{-4x^2} dx=0$?

How Fourier coefficients of $\sum_{k\in \mathbb Z} g(x+ 2k\pi)$ and $\sum_{k\in \mathbb Z} g(x+ (2k+1)\pi) $ are related?

How to prove a cone is convex and closed?

Complex Analysis: Transformations and Equation Solutions

How to compute $\sum_n(2n - \sqrt{n^2+1}-\sqrt{n^2-1})$?

Linearization method or Lyapunov function - example

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