User Borealis

4 votes

1 answer

471 views

Understanding proof that $\mathbb{R}$ is Cauchy complete

asked Jan 29, 2023 at 4:36

2 votes

1 answer

127 views

Evaluate $\lim_{(x,y)\to (0,0)}{\frac{x^3 y}{x^2 - y}}$.

asked Oct 6, 2022 at 0:56

2 votes

2 answers

129 views

Understanding proof that multiplicative inverses exist in $\mathbb{R}$

asked Jan 28, 2023 at 0:54

2 votes

1 answer

35 views

Can $S = \{D_x, xD_x, x^2 D_x, x^3 D_x\}$ be extended to a set generating a Lie algebra?

asked Sep 5 at 4:11

1 vote

1 answer

37 views

Show that $\mathfrak{so}(p,q,\mathbb{R}) = I_{p,q} \mathfrak{so}(n,\mathbb{R})$.

asked Aug 10 at 0:19

1 vote

1 answer

200 views

Passing a test with multiple attempts (conditional probability)

asked Feb 23, 2023 at 2:08

1 vote

1 answer

65 views

Prove that the limit $\lim_{n\to\infty}{n^3}$ does not exist, using the $\varepsilon-N$ definition of a limit.

asked Mar 11, 2022 at 13:01

1 vote

2 answers

83 views

Convergence of $\int_{-\infty}^{\infty}{|x|\sin{x}\,dx}$

asked May 3, 2022 at 22:36

0 votes

2 answers

751 views

Prove that $\lim_{(x,y)\to(0,0)}{\frac{x^ny^m}{x^2+y^2}}=0$ if $n+m>2$.

asked Aug 2, 2022 at 23:54

0 votes

1 answer

131 views

Show that if $\lim_{\textbf{h}\to \textbf{0}}{T(\textbf{h})}=0$, then $\lim_{t\to 0}{T(t\textbf{v})}=0$ for some fixed $\textbf{v}$.

asked Aug 3, 2022 at 0:34

0 votes

1 answer

71 views

Suppose that $f$ is differentiable on $\mathbb{R}$, that $f(1)=1$ and $f(7)=5$. Show that there exists $c\in(0,4)$ such that $f'(c)=\frac{2}{3}$.

asked Apr 10, 2022 at 9:02

0 votes

1 answer

57 views

Prove that $f:(X,d_X)\to (Y,d_Y)$ being continuous at $x\in X$ $\Leftrightarrow$ given any neighbourhood $N$ of $f(x)$, $f^{-1}(N)$ is a nbhd. of $x$

asked Jan 31, 2023 at 9:38

0 votes

1 answer

30 views

Effect of replacing the $L^2$ norm in the definition of multivariable differentiability with the $L^1$ norm.

asked Feb 7, 2023 at 0:33

0 votes

1 answer

45 views

Integral curve equations conversion to cylindrical coordinates

asked Mar 20, 2023 at 6:44

0 votes

1 answer

39 views

Show that two subspaces $X$ and $Y$ of $\ell^1 (\mathbb{R})$ are such that $\overline{X+Y} = \ell^1 (\mathbb{R})$.

asked Apr 27 at 9:34

0 votes

0 answers

44 views

Question about the use of Green's theorem in Do Carmo's proof of the local Gauss-Bonnet theorem.

asked Jul 6 at 4:17

0 votes

1 answer

28 views

Cluster points of $(a_n)_{n=1}^{\infty}$, where $a_1=0$, $a_{2k}=\dfrac{(-1)^k\cdot(3k^2+k)}{k^2+7}$ and $a_{2k+1}=\dfrac{k^4}{k^3+k^2+k+1}$

asked Mar 11, 2022 at 6:34

Stack Exchange Network

17 Questions

Understanding proof that $\mathbb{R}$ is Cauchy complete

Evaluate $\lim_{(x,y)\to (0,0)}{\frac{x^3 y}{x^2 - y}}$.

Understanding proof that multiplicative inverses exist in $\mathbb{R}$

Can $S = \{D_x, xD_x, x^2 D_x, x^3 D_x\}$ be extended to a set generating a Lie algebra?

Show that $\mathfrak{so}(p,q,\mathbb{R}) = I_{p,q} \mathfrak{so}(n,\mathbb{R})$.

Passing a test with multiple attempts (conditional probability)

Prove that the limit $\lim_{n\to\infty}{n^3}$ does not exist, using the $\varepsilon-N$ definition of a limit.

Convergence of $\int_{-\infty}^{\infty}{|x|\sin{x}\,dx}$

Prove that $\lim_{(x,y)\to(0,0)}{\frac{x^ny^m}{x^2+y^2}}=0$ if $n+m>2$.

Show that if $\lim_{\textbf{h}\to \textbf{0}}{T(\textbf{h})}=0$, then $\lim_{t\to 0}{T(t\textbf{v})}=0$ for some fixed $\textbf{v}$.

Suppose that $f$ is differentiable on $\mathbb{R}$, that $f(1)=1$ and $f(7)=5$. Show that there exists $c\in(0,4)$ such that $f'(c)=\frac{2}{3}$.

Prove that $f:(X,d_X)\to (Y,d_Y)$ being continuous at $x\in X$ $\Leftrightarrow$ given any neighbourhood $N$ of $f(x)$, $f^{-1}(N)$ is a nbhd. of $x$

Effect of replacing the $L^2$ norm in the definition of multivariable differentiability with the $L^1$ norm.

Integral curve equations conversion to cylindrical coordinates

Show that two subspaces $X$ and $Y$ of $\ell^1 (\mathbb{R})$ are such that $\overline{X+Y} = \ell^1 (\mathbb{R})$.

Question about the use of Green's theorem in Do Carmo's proof of the local Gauss-Bonnet theorem.

Cluster points of $(a_n)_{n=1}^{\infty}$, where $a_1=0$, $a_{2k}=\dfrac{(-1)^k\cdot(3k^2+k)}{k^2+7}$ and $a_{2k+1}=\dfrac{k^4}{k^3+k^2+k+1}$