User notaMathqueen

4 votes

1 answer

115 views

Proof $f:\frac{(\ln(\frac{\pi}{2x}))^\gamma}{(\cos x)^\beta (\sin x)^\alpha}$ is Lebesgue integrable.

real-analysis lebesgue-integral

asked Aug 10, 2021 at 19:40

3 votes

1 answer

102 views

Composition of uniform function and continuous function

real-analysis

asked Mar 15, 2021 at 19:57

2 votes

1 answer

79 views

Air fan problem - fluid dynamic

fluid-dynamics

asked Jan 15, 2021 at 21:09

2 votes

1 answer

63 views

Proof that in $\mathbb{R}^+$ the function $\frac{1}{1+x}$ is continuous

real-analysis

asked Feb 25, 2021 at 19:01

2 votes

1 answer

39 views

convergences of a row of functions according to a different metric

real-analysis

asked May 5, 2021 at 15:11

2 votes

2 answers

43 views

Hausdorff metric:When A is closed, $[A]_r$ is closed for every $r \in\mathbb{R}^+$.

real-analysis metric-spaces

asked May 6, 2021 at 18:33

2 votes

3 answers

61 views

$V$ with $ A \subseteq V $ and $V_0 = \bigcap_{V \in \mathcal{V}}V$. If $V_0$ is open than $A$ is open.

real-analysis general-topology

asked Jun 10, 2021 at 19:34

2 votes

1 answer

90 views

What is the limit of $\int_{\mathbb{R}}f(x)|\sin( \lambda x)| dx$ for all integrable functions $f:\mathbb{R} \rightarrow \mathbb{C}$?

real-analysis limits lebesgue-integral

asked Aug 17, 2021 at 11:54

1 vote

1 answer

79 views

Does there exist an unique continuous bounded $f$ such that $f(x)= \frac{\sin(f(x))}{2+x^2} - \frac{\cos^2(x)}{1+e^x}$?

real-analysis fixed-point-theorems fixed-points

asked Jun 10, 2021 at 9:14

1 vote

1 answer

61 views

Is $F:\mathbb{R} \rightarrow \mathbb{R}: x \mapsto \int_0^\infty \frac{\arctan(xt)}{1+t^2}dt$ differentiable in $x\not= 0$?

real-analysis integration limits

asked Aug 14, 2021 at 8:09

1 vote

1 answer

40 views

For which values of $p \in \mathbb{R} $ is the integral $I = \int_{0}^{\infty} \frac{x^p}{x^2+a^2}dx$ convergent?

complex-analysis contour-integration complex-integration

asked Jan 24 at 20:59

1 vote

1 answer

37 views

Prove that the family $\{f_n\}$ is normal in $\mathbb{D}\backslash \{0\}$ if and only if f has a removable singularity at $z = 0$.

complex-analysis singularity

asked Jan 26 at 15:11

1 vote

1 answer

27 views

Intersection of open sets and subsets

real-analysis

asked Jun 7, 2021 at 8:16

1 vote

0 answers

63 views

Counterexample that for pointwise limit $lim_{n \rightarrow \infty} f_n(x_n) = f(a)$

real-analysis

asked Mar 15, 2021 at 10:02

0 votes

1 answer

64 views

Is $ f: \mathbb{C} \rightarrow \mathbb{C} : z \rightarrow z|z| $ complex differentiable?

complex-analysis

asked May 19, 2021 at 13:32

0 votes

0 answers

22 views

Is $\mathbb{R}^p \backslash \{0\}$ separable for $2\leq p$

real-analysis metric-spaces

asked May 30, 2021 at 8:05

0 votes

1 answer

49 views

Calculating limits with theorem of Lagrange

real-analysis limits

asked Jun 7, 2021 at 13:06

0 votes

1 answer

46 views

Are the non-empty finite bounded subsets of $\mathbb{R}^2$ complete with respect to the Hausdorff metric?

real-analysis metric-spaces hausdorff-measure

asked Jun 7, 2021 at 15:40

0 votes

1 answer

40 views

What do we know about the set AB if A en B non-empty subsets of $\mathbb{R}_0^+$ with different conditions on A and B

real-analysis general-topology compactness

asked Jun 9, 2021 at 8:20

0 votes

2 answers

58 views

Is $\lim_{x \rightarrow 1} \sum_{n=1}^\infty \frac{nx^2}{n^3+x}=\sum_{n=1}^\infty \frac{n}{n^3 +1}$ correct?

real-analysis sequences-and-series limits

asked Jun 10, 2021 at 6:43

0 votes

0 answers

49 views

proof of total differentiable $f(x,y)=\frac{xy}{(x^2+y^2)^\alpha}$

real-analysis

asked Aug 10, 2021 at 14:46

0 votes

2 answers

27 views

Does $g: \mathbb{R^3} \rightarrow \mathbb{R}: (x,y,z) \rightarrow \frac{f}{1+x^2+y^2+z^2}$ reaches its max/min value

real-analysis continuity maxima-minima

asked Aug 11, 2021 at 8:02

0 votes

1 answer

50 views

Functions between complete metric space and metric space

real-analysis metric-spaces complete-spaces

asked Aug 11, 2021 at 11:50

0 votes

0 answers

50 views

$\Omega_1$ and $\Omega_2$ open and connected in complex plane $\Omega_1 \cap \Omega_2 \neq \emptyset$, $\Omega_1 \cup \Omega_2$ also connected.

complex-analysis connectedness

asked Oct 8, 2021 at 12:18

0 votes

2 answers

48 views

Holomorphic function: proving that $0 \leq f'(x)$ under conditions

complex-analysis

asked Nov 2, 2021 at 15:31

0 votes

1 answer

49 views

Calculate $\int_{\gamma} \frac{1}{(z-1-i)^2} dz$ were $\gamma$ is a smooth curve from 2i to 2

complex-analysis

asked Nov 10, 2021 at 12:39

-4 votes

1 answer

74 views

A function in $\Bbb{Q}$ that is not bounded but is bounded in $\Bbb{R}$ [closed]

real-analysis

asked Mar 17, 2021 at 9:13

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27 Questions

Proof $f:\frac{(\ln(\frac{\pi}{2x}))^\gamma}{(\cos x)^\beta (\sin x)^\alpha}$ is Lebesgue integrable.

Composition of uniform function and continuous function

Air fan problem - fluid dynamic

Proof that in $\mathbb{R}^+$ the function $\frac{1}{1+x}$ is continuous

convergences of a row of functions according to a different metric

Hausdorff metric:When A is closed, $[A]_r$ is closed for every $r \in\mathbb{R}^+$.

$V$ with $ A \subseteq V $ and $V_0 = \bigcap_{V \in \mathcal{V}}V$. If $V_0$ is open than $A$ is open.

What is the limit of $\int_{\mathbb{R}}f(x)|\sin( \lambda x)| dx$ for all integrable functions $f:\mathbb{R} \rightarrow \mathbb{C}$?

Does there exist an unique continuous bounded $f$ such that $f(x)= \frac{\sin(f(x))}{2+x^2} - \frac{\cos^2(x)}{1+e^x}$?

Is $F:\mathbb{R} \rightarrow \mathbb{R}: x \mapsto \int_0^\infty \frac{\arctan(xt)}{1+t^2}dt$ differentiable in $x\not= 0$?

For which values of $p \in \mathbb{R} $ is the integral $I = \int_{0}^{\infty} \frac{x^p}{x^2+a^2}dx$ convergent?

Prove that the family $\{f_n\}$ is normal in $\mathbb{D}\backslash \{0\}$ if and only if f has a removable singularity at $z = 0$.

Intersection of open sets and subsets

Counterexample that for pointwise limit $lim_{n \rightarrow \infty} f_n(x_n) = f(a)$

Is $ f: \mathbb{C} \rightarrow \mathbb{C} : z \rightarrow z|z| $ complex differentiable?

Is $\mathbb{R}^p \backslash \{0\}$ separable for $2\leq p$

Calculating limits with theorem of Lagrange

Are the non-empty finite bounded subsets of $\mathbb{R}^2$ complete with respect to the Hausdorff metric?

What do we know about the set AB if A en B non-empty subsets of $\mathbb{R}_0^+$ with different conditions on A and B

Is $\lim_{x \rightarrow 1} \sum_{n=1}^\infty \frac{nx^2}{n^3+x}=\sum_{n=1}^\infty \frac{n}{n^3 +1}$ correct?

proof of total differentiable $f(x,y)=\frac{xy}{(x^2+y^2)^\alpha}$

Does $g: \mathbb{R^3} \rightarrow \mathbb{R}: (x,y,z) \rightarrow \frac{f}{1+x^2+y^2+z^2}$ reaches its max/min value

Functions between complete metric space and metric space

$\Omega_1$ and $\Omega_2$ open and connected in complex plane $\Omega_1 \cap \Omega_2 \neq \emptyset$, $\Omega_1 \cup \Omega_2$ also connected.

Holomorphic function: proving that $0 \leq f'(x)$ under conditions

Calculate $\int_{\gamma} \frac{1}{(z-1-i)^2} dz$ were $\gamma$ is a smooth curve from 2i to 2

A function in $\Bbb{Q}$ that is not bounded but is bounded in $\Bbb{R}$ [closed]