User Nikolaos Skout

16 votes

Accepted

Why does the limit of this function not exist: $\lim_{x\to \infty} \frac{1}{1+\cos(x)}$

answered Mar 24, 2016 at 18:29

9 votes

Find $f$ if $f(x)\leq x$ and $f(x+y)\leq f(x)+f(y)$ for all $x,~y\in \mathbb{R}.$

answered Jan 23, 2019 at 13:29

6 votes

Accepted

How does the "arc tangent metric" $d(x,y) = | \arctan(x) - \arctan(y)| $ work?

answered Mar 17, 2016 at 21:37

5 votes

The sum of integrals of a function and its inverse: $\int_{0}^{a}f+\int_{f(0)}^{f(a)}f^{-1}=af(a)$

answered Jan 29, 2016 at 15:27

5 votes

Accepted

Series $\sum_\limits{n=0}^\infty \frac{n+1}{n^3-7}$

answered Jan 30, 2016 at 17:19

5 votes

Should I be concerned if I cannot solve most exercises in my textbook?

answered Mar 5, 2016 at 2:52

5 votes

How do I determine $\lim_{x\to 1}(\sqrt[3]{x}-1)/(\sqrt{x}-1)$ without L'Hopital's Rule?

answered Apr 13, 2020 at 14:11

4 votes

Accepted

How do we conclude that $f(x)=0, \forall x\in \mathbb{R}$ ?

answered Feb 1, 2016 at 21:51

4 votes

Using the algebra of limits, calculate the limit $\lim_{n\to \infty}\left(\sqrt{1+n}-\sqrt{n}\right)\sqrt{n+\frac 12}$

answered Mar 16, 2016 at 14:49

4 votes

$\exp(-t^4)$ is not a characteristic function

answered Mar 16, 2016 at 15:36

4 votes

Accepted

Finding the norm of an operator

answered Mar 24, 2016 at 0:11

4 votes

Accepted

How does this Power Series represent this function? My numbers don't come close.

answered Mar 27, 2016 at 21:13

4 votes

Finding a function, given its derivative.

answered Apr 21, 2016 at 13:01

3 votes

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Is $f(x,y) = \frac{x \sin(y^2)}{x^2+y^2}$ with $f(0,0) =0$ continuous?

answered Mar 24, 2016 at 21:44

3 votes

Direct inequality proof of $f(x) = \frac{x}{1+x}$

answered Mar 22, 2016 at 23:08

3 votes

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Can this be proven like this? (Continuity)

answered Mar 8, 2016 at 15:04

3 votes

Accepted

Evaluation of $\lim_{n\rightarrow \infty}\sqrt[n]{\sum^{n}_{k=1}\left(k^{999}+\frac{1}{\sqrt{k}}\right)}$

answered Mar 16, 2016 at 14:20

3 votes

Does $P(EF) = P(E) \cdot P(F)$?

answered Mar 17, 2016 at 17:17

3 votes

?Where does the integral went wrong

answered Mar 19, 2016 at 10:28

3 votes

$f(x) - f'(x) = x^3 + 3x^2 + 3x +1; f(9) =?$

answered Jan 31, 2016 at 15:11

2 votes

Accepted

Show, with the definition, that $\lim_\limits{ (x,y) \to (0,0)} x\sin\frac{1}{y} + y\sin\frac{1}{x}$ exist

answered Jan 30, 2016 at 17:29

2 votes

Accepted

If $\int_a^b f(t) \, dt$ exists and is positive, then there is a subinterval $I$ of $[a,b]$ and $m>0$ such that $f(x) \geq m$ throughout $I$.

answered Feb 15, 2016 at 20:01

2 votes

Let $f:\mathbb R\to \mathbb R$ be continuous, $f(x)\to+\infty$ as $x\to\pm\infty$. Show that $f$ has a minimum.

answered Feb 18, 2016 at 0:58

2 votes

Accepted

Independence of $\sigma$-algebras

answered Feb 23, 2016 at 12:57

2 votes

Accepted

Graphical representation of double integral

answered Mar 22, 2016 at 23:25

2 votes

Accepted

Proving Corollary to Riesz's Lemma

answered Mar 16, 2016 at 15:47

2 votes

How to show $\text{Im}~ \theta=\Bbb{Q} [\sqrt 2]$ for a homomorphism?

answered Mar 27, 2016 at 16:21

2 votes

Solve $\frac{dy}{dx}=x^2e^{-4x}-4y$

answered Mar 28, 2016 at 21:58

2 votes

The dimension of subspace

answered Oct 15, 2016 at 20:42

2 votes

Accepted

How to prove that functions of independent variables are independent?

answered Feb 10, 2017 at 11:31

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83 Answers

Why does the limit of this function not exist: $\lim_{x\to \infty} \frac{1}{1+\cos(x)}$

Find $f$ if $f(x)\leq x$ and $f(x+y)\leq f(x)+f(y)$ for all $x,~y\in \mathbb{R}.$

How does the "arc tangent metric" $d(x,y) = | \arctan(x) - \arctan(y)| $ work?

The sum of integrals of a function and its inverse: $\int_{0}^{a}f+\int_{f(0)}^{f(a)}f^{-1}=af(a)$

Series $\sum_\limits{n=0}^\infty \frac{n+1}{n^3-7}$

Should I be concerned if I cannot solve most exercises in my textbook?

How do I determine $\lim_{x\to 1}(\sqrt[3]{x}-1)/(\sqrt{x}-1)$ without L'Hopital's Rule?

How do we conclude that $f(x)=0, \forall x\in \mathbb{R}$ ?

Using the algebra of limits, calculate the limit $\lim_{n\to \infty}\left(\sqrt{1+n}-\sqrt{n}\right)\sqrt{n+\frac 12}$

$\exp(-t^4)$ is not a characteristic function

Finding the norm of an operator

How does this Power Series represent this function? My numbers don't come close.

Finding a function, given its derivative.

Is $f(x,y) = \frac{x \sin(y^2)}{x^2+y^2}$ with $f(0,0) =0$ continuous?

Direct inequality proof of $f(x) = \frac{x}{1+x}$

Can this be proven like this? (Continuity)

Evaluation of $\lim_{n\rightarrow \infty}\sqrt[n]{\sum^{n}_{k=1}\left(k^{999}+\frac{1}{\sqrt{k}}\right)}$

Does $P(EF) = P(E) \cdot P(F)$?

?Where does the integral went wrong

$f(x) - f'(x) = x^3 + 3x^2 + 3x +1; f(9) =?$

Show, with the definition, that $\lim_\limits{ (x,y) \to (0,0)} x\sin\frac{1}{y} + y\sin\frac{1}{x}$ exist

If $\int_a^b f(t) \, dt$ exists and is positive, then there is a subinterval $I$ of $[a,b]$ and $m>0$ such that $f(x) \geq m$ throughout $I$.

Let $f:\mathbb R\to \mathbb R$ be continuous, $f(x)\to+\infty$ as $x\to\pm\infty$. Show that $f$ has a minimum.

Independence of $\sigma$-algebras

Graphical representation of double integral

Proving Corollary to Riesz's Lemma

How to show $\text{Im}~ \theta=\Bbb{Q} [\sqrt 2]$ for a homomorphism?

Solve $\frac{dy}{dx}=x^2e^{-4x}-4y$

The dimension of subspace

How to prove that functions of independent variables are independent?