User learningmaths - Mathematics Stack Exchange

6 votes

2 answers

181 views

What is the domain of $\left(\frac{x^2-3}{x^2+4}\right)^{2x^3}$?

asked Mar 7, 2023 at 0:05

5 votes

0 answers

273 views

Proving that limits at infinity are unique help

asked Feb 2, 2022 at 22:31

3 votes

0 answers

423 views

How to prove that $h(x):=\int_a^bg(t-x)f(t)dt$ is Lipschitz continuous?

asked Feb 17, 2022 at 1:37

1 vote

1 answer

63 views

How to prove that $f:[0,1]\cup[2,4]\rightarrow \mathbb R$ is continuous using topology?

asked Mar 20, 2022 at 9:37

1 vote

0 answers

45 views

Proving that $d(x,y)=0$ if and only if $x=y$ for a given set of continuous functions

asked May 14, 2022 at 0:32

1 vote

2 answers

225 views

Prove that $1/x^2$ is not uniformly continuous on $(0,\infty)$ using $\varepsilon$-$\delta$ arguments

asked Jul 12, 2022 at 10:12

1 vote

2 answers

195 views

Can we compute this integral $\int_0^{2\pi} \frac{1}{5+3 \cos x} dx$ using an antiderivative defined on $\mathbb R$? [duplicate]

asked Jul 22, 2022 at 0:55

1 vote

2 answers

302 views

If $N\in \mathbb N$ and $b$ irrational, why are there finitely many rationals $r=p/q$, with $p,q$ coprime & $0<q\leq N$, in the interval $(b-1,b+1)$?

asked Feb 4, 2022 at 21:04

1 vote

1 answer

112 views

Infinite limit at infinity complex variables using definition

asked Dec 22, 2022 at 10:16

1 vote

0 answers

54 views

For classification of quadratic forms with orthogonal diagonalization, why do we need a rotation?

asked Feb 3, 2023 at 9:32

1 vote

2 answers

148 views

Continuity of partial derivatives of $f(x,y) =\dfrac{xy(x^2-y^2)}{x^2+y^2}$ if $(x,y)\neq 0$ and $f(x,y)= 0$ if $(x,y) = (0,0).$

asked Jun 2, 2023 at 9:53

0 votes

1 answer

45 views

Is it possible to define a function of two inputs is also a function of one input at the same time?

asked Oct 22, 2023 at 21:12

0 votes

1 answer

88 views

What is the meaning of $\mathbb C$-linearizarion?

asked Aug 3, 2022 at 10:30

0 votes

0 answers

55 views

Why $\lim_{(x,y)\to (0,0)}\frac{x}{y^{2/3}}$ does not exist?

asked Nov 25, 2022 at 0:34

0 votes

1 answer

64 views

Limit of $\exp(z)$ as $z\to \infty$ for specific domains

asked Dec 20, 2022 at 23:14

0 votes

1 answer

34 views

How to prove of $\lim \frac{1}{|x|+1}=0$ as $x$ goes to $-\infty$?

asked Mar 22, 2022 at 6:18

0 votes

3 answers

179 views

Is a bounded polynomial constant? [duplicate]

asked Apr 2, 2022 at 3:20

0 votes

2 answers

102 views

How to compute the norm operator of operators in $L(\mathbb R^2)$

asked Apr 13, 2022 at 8:02

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18 Questions

What is the domain of $\left(\frac{x^2-3}{x^2+4}\right)^{2x^3}$?

Proving that limits at infinity are unique help

How to prove that $h(x):=\int_a^bg(t-x)f(t)dt$ is Lipschitz continuous?

How to prove that $f:[0,1]\cup[2,4]\rightarrow \mathbb R$ is continuous using topology?

Proving that $d(x,y)=0$ if and only if $x=y$ for a given set of continuous functions

Prove that $1/x^2$ is not uniformly continuous on $(0,\infty)$ using $\varepsilon$-$\delta$ arguments

Can we compute this integral $\int_0^{2\pi} \frac{1}{5+3 \cos x} dx$ using an antiderivative defined on $\mathbb R$? [duplicate]

If $N\in \mathbb N$ and $b$ irrational, why are there finitely many rationals $r=p/q$, with $p,q$ coprime & $0<q\leq N$, in the interval $(b-1,b+1)$?

Infinite limit at infinity complex variables using definition

For classification of quadratic forms with orthogonal diagonalization, why do we need a rotation?

Continuity of partial derivatives of $f(x,y) =\dfrac{xy(x^2-y^2)}{x^2+y^2}$ if $(x,y)\neq 0$ and $f(x,y)= 0$ if $(x,y) = (0,0).$

Is it possible to define a function of two inputs is also a function of one input at the same time?

What is the meaning of $\mathbb C$-linearizarion?

Why $\lim_{(x,y)\to (0,0)}\frac{x}{y^{2/3}}$ does not exist?

Limit of $\exp(z)$ as $z\to \infty$ for specific domains

How to prove of $\lim \frac{1}{|x|+1}=0$ as $x$ goes to $-\infty$?

Is a bounded polynomial constant? [duplicate]

How to compute the norm operator of operators in $L(\mathbb R^2)$