Question

How to solve MIT Integration Bee $2023$: $\int_0^{100} \lfloor x\rfloor x\lceil x\rceil dx$

score 350 · Answer 1 · 2026-04-16 10:31:53

350

Views

How to solve MIT Integration Bee $2023$: $\int_0^{100} \lfloor x\rfloor x\lceil x\rceil dx$

Published on 16 Apr 2026 - 10:31

score 118 · Answer 2 · 2026-05-05 14:28:00

118

Views

But will $(\tan(x))^{\ln(\sin(x))}$ ever equal $(\ln(\cot(x)))^{\cos(x)}$

Published on 05 May 2026 - 14:28

score 86 · Answer 3 · 2026-04-15 01:41:25

86

Views

Prove that $(\mathbb{Q}^*, \times )$ is not cyclic (compare my solution to textbook solution)

Published on 15 Apr 2026 - 1:41

score 50 · Answer 4 · 2026-04-16 07:20:44

50

Views

If $[0, 1)\times\dots\times [0,1)\cap\mathbb{Q}^d\subset\bigcup_{j=1}^n I_j,$ then $[0, 1)\times\dots\times [0,1)\subset\bigcup_{j=1}^n I_j.$

Published on 16 Apr 2026 - 7:20

score 186 · Answer 5 · 2026-04-16 05:27:21

186

Views

Proof verification: $a$ and $b$ that satisfy $\frac{a+b}{a} = \frac{b}{a+b}$ cannot be both real.

Published on 16 Apr 2026 - 5:27

score 21 · Answer 6 · 2026-04-07 16:43:55

21

Views

Formula for bulk buying with value based on available stock

Published on 07 Apr 2026 - 16:43

score 44 · Answer 7 · 2026-04-12 14:39:01

44

Views

Show that if a set $A$ of integers is bounded above, then $A$ has a largest element.

Published on 12 Apr 2026 - 14:39

score 33 · Answer 8 · 2026-04-15 09:39:27

33

Views

Proving a set of hypotheses is inconsistent

Published on 15 Apr 2026 - 9:39

score 126 · Answer 9 · 2026-04-14 01:37:15

126

Views

Coadjoint orbits coincide with symplectic leaves, Dufour's proof

Published on 14 Apr 2026 - 1:37

score 48 · Answer 10 · 2026-03-26 06:33:36

48

Views

Brezis' exercise 5.25.3

Published on 26 Mar 2026 - 6:33

score 124 · Answer 11 · 2026-04-15 23:14:37

124

Views

Identify the generated set $S$, starting from $1$ and $2$, by all $3x+y$ with distinct $x,y \in S$

Published on 15 Apr 2026 - 23:14

score 107 · Answer 12 · 2026-04-17 07:53:19

107

Views

Show that $A\star B=\{ab:(a,b)\in A\times B\}$ in $\mathcal P(X)$ is associative or commutative iff $$ in $X$ is it.

Published on 17 Apr 2026 - 7:53

score 122 · Answer 13 · 2026-04-17 18:50:41

122

Views

Prove that $\pi=2i\ln\left(\frac{1-i}{1+i}\right)$

Published on 17 Apr 2026 - 18:50

score 139 · Answer 14 · 2026-04-16 09:05:16

Find the number of distinct positive integers that can be formed using 0, 1, 2 and 4, where each of these integers is used at most once.

score 120 · Answer 15 · 2026-04-13 08:36:38

120

Views

Mathematical Statistics: Exercises and Solutions by Jun Shao Chapter $1$ Exercise $6$

Published on 13 Apr 2026 - 8:36

List Question

How to solve MIT Integration Bee $2023$: $\int_0^{100} \lfloor x\rfloor x\lceil x\rceil dx$

But will $(\tan(x))^{\ln(\sin(x))}$ ever equal $(\ln(\cot(x)))^{\cos(x)}$

Prove that $(\mathbb{Q}^*, \times )$ is not cyclic (compare my solution to textbook solution)

If $[0, 1)\times\dots\times [0,1)\cap\mathbb{Q}^d\subset\bigcup_{j=1}^n I_j,$ then $[0, 1)\times\dots\times [0,1)\subset\bigcup_{j=1}^n I_j.$

Proof verification: $a$ and $b$ that satisfy $\frac{a+b}{a} = \frac{b}{a+b}$ cannot be both real.

Formula for bulk buying with value based on available stock

Show that if a set $A$ of integers is bounded above, then $A$ has a largest element.

Proving a set of hypotheses is inconsistent

Coadjoint orbits coincide with symplectic leaves, Dufour's proof

Brezis' exercise 5.25.3

Identify the generated set $S$, starting from $1$ and $2$, by all $3x+y$ with distinct $x,y \in S$

Show that $A\star B=\{ab:(a,b)\in A\times B\}$ in $\mathcal P(X)$ is associative or commutative iff $$ in $X$ is it.

Prove that $\pi=2i\ln\left(\frac{1-i}{1+i}\right)$

Find the number of distinct positive integers that can be formed using 0, 1, 2 and 4, where each of these integers is used at most once.

Mathematical Statistics: Exercises and Solutions by Jun Shao Chapter $1$ Exercise $6$

Trending Questions

Popular # Hahtags

Popular Questions