Question

Determine where a function is local injective

score 209 · Answer 1 · 2018-05-21 19:55:11

209

Views

Determine where a function is local injective

Published on 21 May 2018 - 19:55

score 44 · Answer 2 · 2026-04-02 01:35:36

44

Views

Show $f:[1,\infty[\rightarrow[1,\infty[, x\mapsto x^x$ is bijective and continuous, and show continuity for $f^{-1}$

Published on 02 Apr 2026 - 1:35

score 138 · Answer 3 · 2018-05-22 01:19:19

138

Views

Limit of a Function that is the Product of two Functions.

Published on 22 May 2018 - 1:19

score 43 · Answer 4 · 2018-05-22 02:29:56

43

Views

Find the limit of $d_1 = 1, d_{n+1}=1+\frac{d_n}{3}$

Published on 22 May 2018 - 2:29

score 54 · Answer 5 · 2026-03-25 18:50:37

54

Views

Given $F(x) = \int_a^xf(t)dt$, for $f \in L^p([a,b])$, prove a uniform bound of $\sum_{i=0}^{n-1} \frac{|F(x_{i+1})-F(x_i)|^p}{(x_{i+1}-x_i)^{p-1}}$

Published on 25 Mar 2026 - 18:50

score 300 · Answer 6 · 2018-05-22 03:35:44

300

Views

Is Hilbert's space-filling curve measure preserving?

Published on 22 May 2018 - 3:35

score 47 · Answer 7 · 2026-03-28 09:57:14

47

Views

Sketch $M=\{re^{i\phi}:r\in(1,2],\phi\in[0,\pi)\}$ and give its closure $\overline{M}$. Is $M$ compact?

Published on 28 Mar 2026 - 9:57

score 108 · Answer 8 · 2026-03-28 09:57:12

108

Views

Let $K\subseteq\mathbb{C}$ be compact and non-empty. Show there exists a $z\in K$ such that $|z|=\inf\{|w|:w\in K\}$.

Published on 28 Mar 2026 - 9:57

score 100 · Answer 9 · 2026-03-25 14:19:36

100

Views

Binary branching process with exponential distribution

Published on 25 Mar 2026 - 14:19

score 87 · Answer 10 · 2018-05-22 15:21:27

87

Views

Does there exists a finite index non-trivial subgroup of $\mathbb{C}^*$

Published on 22 May 2018 - 15:21

score 74 · Answer 11 · 2018-05-22 18:40:58

74

Views

Second-order differential equation with initial conditions

Published on 22 May 2018 - 18:40

score 188 · Answer 12 · 2018-05-22 18:57:55

188

Views

Prove that $Z-(Y-X)=X\cup(Z-Y)$ if $X\subset Y\subset Z$

Published on 22 May 2018 - 18:57

score 326 · Answer 13 · 2026-03-27 00:09:50

326

Views

Using the Boolean identities, simplify the following expressions:

Published on 27 Mar 2026 - 0:09

score 30 · Answer 14 · 2018-05-23 04:37:06

30

Views

$(ab,ac)=a(b,c) , a >0$

Published on 23 May 2018 - 4:37

score 40 · Answer 15 · 2018-05-23 09:59:35

40

Views

Prove that the sequence is bounded (proof verification)

Published on 23 May 2018 - 9:59

List Question

Determine where a function is local injective

Show $f:[1,\infty[\rightarrow[1,\infty[, x\mapsto x^x$ is bijective and continuous, and show continuity for $f^{-1}$

Limit of a Function that is the Product of two Functions.

Find the limit of $d_1 = 1, d_{n+1}=1+\frac{d_n}{3}$

Given $F(x) = \int_a^xf(t)dt$, for $f \in L^p([a,b])$, prove a uniform bound of $\sum_{i=0}^{n-1} \frac{|F(x_{i+1})-F(x_i)|^p}{(x_{i+1}-x_i)^{p-1}}$

Is Hilbert's space-filling curve measure preserving?

Sketch $M=\{re^{i\phi}:r\in(1,2],\phi\in[0,\pi)\}$ and give its closure $\overline{M}$. Is $M$ compact?

Let $K\subseteq\mathbb{C}$ be compact and non-empty. Show there exists a $z\in K$ such that $|z|=\inf\{|w|:w\in K\}$.

Binary branching process with exponential distribution

Does there exists a finite index non-trivial subgroup of $\mathbb{C}^*$

Second-order differential equation with initial conditions

Prove that $Z-(Y-X)=X\cup(Z-Y)$ if $X\subset Y\subset Z$

Using the Boolean identities, simplify the following expressions:

$(ab,ac)=a(b,c) , a >0$

Prove that the sequence is bounded (proof verification)

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