User Reuben - Mathematics Stack Exchange

7 votes

2 answers

489 views

Let $\alpha$ be an increasing function on $[a,b]$. Show that $\int^a_b\alpha d \alpha = \frac{1}{2}[\alpha (b)^2 - \alpha(a)^2]$

asked Jul 26, 2022 at 1:10

5 votes

2 answers

672 views

Can there be more than one global maximums of a function?

asked May 15 at 14:13

4 votes

2 answers

250 views

When we classify a polynomial as binomial, trinomial, etc., do we have to simplify it first?

asked Jun 1 at 7:53

4 votes

2 answers

189 views

How do we prove by contradiction that, if $\langle x,y\rangle = \langle x,z\rangle$ for all $x$, then $y=z$?

asked Jul 25, 2022 at 0:48

3 votes

2 answers

927 views

Counting Problem: A group of 30 people consists of 15 women and 15 men, How many ways to:

asked Mar 15, 2020 at 6:30

3 votes

1 answer

94 views

Help with understanding Cauchy sequences?

asked Apr 28, 2022 at 14:08

3 votes

1 answer

79 views

What is meant by an if and only if statement with 2 conditions?

asked May 25, 2022 at 1:00

2 votes

1 answer

846 views

prove that $\operatorname{Int}(A \cap B)= \operatorname{Int}(A) \cap \operatorname{Int}(B)$

asked Apr 17, 2022 at 0:23

2 votes

1 answer

89 views

Show that a subset of $X$ is open in $(X,d)$ if and only if it is open in $(X,\rho)$

asked Apr 22, 2022 at 9:02

2 votes

3 answers

758 views

Prove that $\operatorname{int}(A)$, $\operatorname{int}(X\backslash A)$ and $\partial(A)$ are pairwise disjoint sets whose union is $X$.

asked Apr 23, 2022 at 11:39

2 votes

2 answers

93 views

Why is there a change in inequality from ">" to "$\geq$" in this example?

asked Jun 27, 2022 at 1:55

1 vote

1 answer

31 views

Show that $S$ is a bounded subset of $X$ if it converges to $p$

asked Apr 25, 2022 at 13:14

1 vote

0 answers

17 views

$f[a_1] = G$ means $a_1 \subseteq f^{-1}[G]$ for functions on metric spaces?

asked Jun 21, 2022 at 14:31

1 vote

0 answers

49 views

Help with use of Fundamental Lemma of Calculus of Variations in deriving eluer lagrange equation

asked Nov 15, 2022 at 0:36

1 vote

1 answer

177 views

Help with Parallel transport of a vector

asked Sep 4, 2023 at 13:51

1 vote

1 answer

181 views

Let $A$ be a subset of a metric space with $\partial A = \varnothing$. Show that $A$ is both open and closed

asked Apr 18, 2022 at 2:08

1 vote

2 answers

91 views

Help with a simple theorem proof involving supremum

asked Apr 19, 2022 at 18:01

1 vote

1 answer

40 views

Help with a simple theorem proof involving supremum(part 2)

asked Apr 20, 2022 at 0:26

1 vote

1 answer

763 views

Proving that the complex numbers: additive/multiplicative identity is unique

asked Mar 9, 2022 at 11:37

1 vote

1 answer

515 views

Fundamental matrices are non-singular for all $t$

asked May 25, 2022 at 9:50

1 vote

0 answers

73 views

Why is a normalized fundamental matrix non-singular for all t?

asked May 25, 2022 at 23:37

1 vote

0 answers

50 views

Help with Liouville's formula (putting it into "easier words")

asked May 26, 2022 at 11:40

1 vote

2 answers

182 views

Let $\{a_n\}$ and $\{b_n\}$ be Cauchy sequences. Let $s_n = d(a_n,b_n)$. Show that $\{s_n\}$converges

asked Apr 29, 2022 at 23:45

1 vote

0 answers

86 views

Suppose that $|a_n|<2$ and $|a_{n+2}−a_{n+1}|\leq\frac{1}{8}|a_{n+1}^2−a_n^2|$, prove that $\{a_n\}$ converges.

asked Apr 30, 2022 at 5:59

1 vote

0 answers

70 views

Show that $(X,d)$ is complete if and only if $(X,\overline{d})$ is complete

asked Apr 30, 2022 at 16:40

1 vote

1 answer

58 views

Suppose that $|a_n|<2$ and $|a_{n+2}−a_{n+1}|\leq\frac{1}{8}|a_{n+1}^2−a_n^2|$, prove that $\{a_n\}$ converges. (Part 2)

asked Apr 30, 2022 at 21:39

1 vote

0 answers

31 views

When can we just use the normal distribution properties?

asked May 25 at 21:25

1 vote

1 answer

69 views

Proof that $f′(0)=0$ when $x=0$ is a local extremum(taylor method)

asked Apr 20, 2023 at 16:30

0 votes

0 answers

58 views

What does $\nabla_k$ mean?

asked May 1, 2023 at 5:22

0 votes

0 answers

63 views

Why is the integrand bounded on [$0,b$] when integrand can be infinite for $x=0$ [duplicate]

asked Aug 3, 2023 at 16:53

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57 Questions

Let $\alpha$ be an increasing function on $[a,b]$. Show that $\int^a_b\alpha d \alpha = \frac{1}{2}[\alpha (b)^2 - \alpha(a)^2]$

Can there be more than one global maximums of a function?

When we classify a polynomial as binomial, trinomial, etc., do we have to simplify it first?

How do we prove by contradiction that, if $\langle x,y\rangle = \langle x,z\rangle$ for all $x$, then $y=z$?

Counting Problem: A group of 30 people consists of 15 women and 15 men, How many ways to:

Help with understanding Cauchy sequences?

What is meant by an if and only if statement with 2 conditions?

prove that $\operatorname{Int}(A \cap B)= \operatorname{Int}(A) \cap \operatorname{Int}(B)$

Show that a subset of $X$ is open in $(X,d)$ if and only if it is open in $(X,\rho)$

Prove that $\operatorname{int}(A)$, $\operatorname{int}(X\backslash A)$ and $\partial(A)$ are pairwise disjoint sets whose union is $X$.

Why is there a change in inequality from ">" to "$\geq$" in this example?

Show that $S$ is a bounded subset of $X$ if it converges to $p$

$f[a_1] = G$ means $a_1 \subseteq f^{-1}[G]$ for functions on metric spaces?

Help with use of Fundamental Lemma of Calculus of Variations in deriving eluer lagrange equation

Help with Parallel transport of a vector

Let $A$ be a subset of a metric space with $\partial A = \varnothing$. Show that $A$ is both open and closed

Help with a simple theorem proof involving supremum

Help with a simple theorem proof involving supremum(part 2)

Proving that the complex numbers: additive/multiplicative identity is unique

Fundamental matrices are non-singular for all $t$

Why is a normalized fundamental matrix non-singular for all t?

Help with Liouville's formula (putting it into "easier words")

Let $\{a_n\}$ and $\{b_n\}$ be Cauchy sequences. Let $s_n = d(a_n,b_n)$. Show that $\{s_n\}$converges

Suppose that $|a_n|<2$ and $|a_{n+2}−a_{n+1}|\leq\frac{1}{8}|a_{n+1}^2−a_n^2|$, prove that $\{a_n\}$ converges.

Show that $(X,d)$ is complete if and only if $(X,\overline{d})$ is complete

Suppose that $|a_n|<2$ and $|a_{n+2}−a_{n+1}|\leq\frac{1}{8}|a_{n+1}^2−a_n^2|$, prove that $\{a_n\}$ converges. (Part 2)

When can we just use the normal distribution properties?

Proof that $f′(0)=0$ when $x=0$ is a local extremum(taylor method)

What does $\nabla_k$ mean?

Why is the integrand bounded on [$0,b$] when integrand can be infinite for $x=0$ [duplicate]