Question

Which function satisfies $: \mathbb R → [−2, 2]$ with $((0))^ 2 + ( ′ (0))^ 2 = 85$,also $f$ is twice differentiable?

score 615 · Answer 1 · 2026-03-24 23:54:57

615

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Which function satisfies $: \mathbb R → [−2, 2]$ with $((0))^ 2 + ( ′ (0))^ 2 = 85$,also $f$ is twice differentiable?

Published on 24 Mar 2026 - 23:54

score 449 · Answer 2 · 2026-03-25 00:41:24

449

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Cauchy problem for diffusion equation and condition $x^2$ if $x\in [0,1]$

Published on 25 Mar 2026 - 0:41

score 568 · Answer 3 · 2026-03-25 04:43:48

568

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Wave problem $u_{tt}=u_{xx}-u_t, 0\le x\le 2\pi$ with $u(x,0)=\phi(x)$, $u_t(x,0)=\psi(x)$ and $u(0,t)=u(2\pi,t)=0$

Published on 25 Mar 2026 - 4:43

score 805 · Answer 4 · 2018-06-26 05:45:31

805

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Proving the Trig Identities $\sin(-\theta)=-\sin(\theta)$ and $\cos(-\theta)=\cos(\theta)$

Published on 26 Jun 2018 - 5:45

score 854 · Answer 5 · 2018-06-27 10:25:54

854

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Proof verification : $X_n \to X$ in distribution, $Y_n \to 0$ in probability $\implies$ $X_nY_n \to 0$ in probability

Published on 27 Jun 2018 - 10:25

score 90 · Answer 6 · 2018-06-27 20:52:41

90

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$ \int^1_0 \max\{f_1(x), . . . , f_n(x)\} \, dx \leq C $, $f_n \geq 0$ and $f_n \to 0$, then $f_n \to 0$ in $L^1(0,1)$

Published on 27 Jun 2018 - 20:52

score 1.3k · Answer 7 · 2026-03-22 03:47:37

1.3k

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Proving $x^2+x+1\gt0$

Published on 22 Mar 2026 - 3:47

score 171 · Answer 8 · 2026-03-25 12:49:57

171

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Prove that $ \liminf_{t\to+\infty} f'(t)\leq 0 \leq \limsup_{t\to+\infty} f'(t) $

Published on 25 Mar 2026 - 12:49

score 604 · Answer 9 · 2026-03-25 20:12:41

604

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$f_n \rightharpoonup f$, $g_n \to g$ in measure, $\|g_n\|_{L^\infty} \leq M$, then $f_n g_n \rightharpoonup fg$,

Published on 25 Mar 2026 - 20:12

score 51 · Answer 10 · 2026-03-26 01:04:32

51

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Formal proof of $\sup \limits_{0<r} f(r) = \sup \limits_{0<R} \sup \limits_{0<r<R} f(r)$

Published on 26 Mar 2026 - 1:04

score 138 · Answer 11 · 2026-03-25 20:11:18

138

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If $\phi: [0,\, 1] \to X $ be a sequentially weakly continuous, then $f(t) = \|φ(t)\| $ is bounded

Published on 25 Mar 2026 - 20:11

score 52 · Answer 12 · 2018-07-01 13:34:23

52

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The following function is only continuous at one point. Is it differentiable at that point?

Published on 01 Jul 2018 - 13:34

score 41 · Answer 13 · 2018-07-01 14:37:58

41

Views

If $ \big| \int^b_a f(t,x)- f(s,x)\,\, dx\big|\leq C(b-a)(t-s)$, then $|f(t, x) − f(s, x)| \leq C(t − s)$

Published on 01 Jul 2018 - 14:37

score 143 · Answer 14 · 2018-07-02 05:29:31

143

Views

Confusion on Laszlo Kalmar's PL completeness proof

Published on 02 Jul 2018 - 5:29

score 152 · Answer 15 · 2026-03-25 13:56:17

152

Views

$\forall k,n \in\mathbb N:k\in n\iff k\subsetneq n$ [Proof Verification and Suggestion for shorter or simpler proof]

Published on 25 Mar 2026 - 13:56

List Question

Which function satisfies $: \mathbb R → [−2, 2]$ with $((0))^ 2 + ( ′ (0))^ 2 = 85$,also $f$ is twice differentiable?

Cauchy problem for diffusion equation and condition $x^2$ if $x\in [0,1]$

Wave problem $u_{tt}=u_{xx}-u_t, 0\le x\le 2\pi$ with $u(x,0)=\phi(x)$, $u_t(x,0)=\psi(x)$ and $u(0,t)=u(2\pi,t)=0$

Proving the Trig Identities $\sin(-\theta)=-\sin(\theta)$ and $\cos(-\theta)=\cos(\theta)$

Proof verification : $X_n \to X$ in distribution, $Y_n \to 0$ in probability $\implies$ $X_nY_n \to 0$ in probability

$ \int^1_0 \max\{f_1(x), . . . , f_n(x)\} \, dx \leq C $, $f_n \geq 0$ and $f_n \to 0$, then $f_n \to 0$ in $L^1(0,1)$

Proving $x^2+x+1\gt0$

Prove that $ \liminf_{t\to+\infty} f'(t)\leq 0 \leq \limsup_{t\to+\infty} f'(t) $

$f_n \rightharpoonup f$, $g_n \to g$ in measure, $\|g_n\|_{L^\infty} \leq M$, then $f_n g_n \rightharpoonup fg$,

Formal proof of $\sup \limits_{0<r} f(r) = \sup \limits_{0<R} \sup \limits_{0<r<R} f(r)$

If $\phi: [0,\, 1] \to X $ be a sequentially weakly continuous, then $f(t) = \|φ(t)\| $ is bounded

The following function is only continuous at one point. Is it differentiable at that point?

If $ \big| \int^b_a f(t,x)- f(s,x)\,\, dx\big|\leq C(b-a)(t-s)$, then $|f(t, x) − f(s, x)| \leq C(t − s)$

Confusion on Laszlo Kalmar's PL completeness proof

$\forall k,n \in\mathbb N:k\in n\iff k\subsetneq n$ [Proof Verification and Suggestion for shorter or simpler proof]

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