User gniourf_gniourf

27 votes

Show that $f^{(n)}(0)=0$ for $n=0,1,2, \dots$

answered Jun 29, 2014 at 16:49

14 votes

Accepted

Is a probability density function necessarily a $L^2$ function?

answered Apr 16, 2014 at 17:25

14 votes

Accepted

Why do we chose exponential function as a trial solution for second order linear differential equation with constant coefficient?

answered Jul 4, 2014 at 18:11

12 votes

Accepted

Show that boundary of a closed set is nowhere dense

answered Feb 11, 2015 at 10:44

11 votes

Accepted

Prove that if $\sum a_n$ converges, then $na_n \to 0$.

answered Feb 10, 2016 at 19:07

11 votes

Evaluation of $\int_{\frac{1}{2014}}^{2014} \frac{\tan^{-1}x}{x} dx$

answered Feb 18, 2016 at 19:35

10 votes

Accepted

How to explain this quirk of the chain rule?

answered Jun 28, 2014 at 20:03

9 votes

Accepted

Computing a Lie Bracket: General Questions

answered Apr 13, 2014 at 18:26

8 votes

Accepted

Integral of $\int_{\mathbb{R}}e^{-\frac{x^{2}}{2}}\left(\cos\left(\pi nx\right)\right)dx$

answered Feb 9, 2016 at 13:53

7 votes

Accepted

Killing form on some Lie algebra $L$ is zero. Is $L$ necessarily nilpotent?

answered Sep 25, 2014 at 14:11

7 votes

Find the Jordan normal form of a nilpotent matrix $N$ given the dimensions of the kernels of $N, N^2, N^3$

answered Feb 8, 2016 at 12:20

7 votes

A finite field extension of $\mathbb R$ is either $\mathbb R$ or isomorphic to $\mathbb C$

answered Mar 21, 2015 at 14:33

7 votes

$A$ is diagonalizable and $A^3 = A^2$

answered Jul 2, 2014 at 13:48

7 votes

Accepted

$f\colon(0,\infty)\to \mathbb R$ be continuous ; $f(x)\le f(nx) , \forall n \in \mathbb N , \forall x >0$ , then $\lim_{x\to \infty} f(x)$ exists?

answered Dec 18, 2016 at 15:53

6 votes

Accepted

A simple function equation

answered Jun 28, 2014 at 16:17

6 votes

Can the limit $\lim_{h \to 0}\frac{f(x + h) - 2f(x) + f(x - h)}{h^2}$ exist if $f'(x)$ does not exist at $x$?

answered Jul 3, 2014 at 14:20

6 votes

Show $\lim_{n_\rightarrow \infty}\int_0^\infty ne^{-\frac{2n^2x^2}{x + 1}}dx = \infty$

answered Jun 27, 2014 at 16:58

5 votes

Accepted

Find linear transformation given kernel

answered Apr 13, 2014 at 17:19

5 votes

Topology that makes the finite set $X =\{1,2,3,4,5\}$ a regular space

answered Dec 19, 2016 at 18:35

5 votes

Accepted

The set of all limits of sub-series of an absolute convergent series

answered Dec 18, 2016 at 12:36

5 votes

Grandi's series with 3 numbers

answered Dec 18, 2016 at 13:04

4 votes

Accepted

What is the value of $\lim _{x\to 0}\left\lfloor\frac{\tan x \sin x}{x^2}\right\rfloor$

answered Feb 18, 2016 at 17:19

4 votes

Accepted

Proof of minimum eigenvalue of non-symmetric matrix with real eigenvalues

answered Dec 24, 2017 at 19:11

4 votes

Accepted

When are these quotient rings isomorphic?

answered Dec 4, 2016 at 13:22

4 votes

Accepted

Composition of convex and power function

answered Jun 27, 2014 at 16:28

4 votes

Accepted

Chain rule question total differentiation

answered Jun 29, 2014 at 11:21

4 votes

Accepted

Divergence Theorem Question

answered Jul 3, 2014 at 18:19

3 votes

Find all real and continuous functions that are a 3-involution.

answered Feb 20, 2016 at 13:43

3 votes

Showing that a derivable function $f$ (satisfying some conditions) is null.

answered Feb 16, 2016 at 22:25

3 votes

Accepted

Pointwise and uniform convergence of sequence of functions

answered Jun 29, 2014 at 14:42

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100 Answers

Show that $f^{(n)}(0)=0$ for $n=0,1,2, \dots$

Is a probability density function necessarily a $L^2$ function?

Why do we chose exponential function as a trial solution for second order linear differential equation with constant coefficient?

Show that boundary of a closed set is nowhere dense

Prove that if $\sum a_n$ converges, then $na_n \to 0$.

Evaluation of $\int_{\frac{1}{2014}}^{2014} \frac{\tan^{-1}x}{x} dx$

How to explain this quirk of the chain rule?

Computing a Lie Bracket: General Questions

Integral of $\int_{\mathbb{R}}e^{-\frac{x^{2}}{2}}\left(\cos\left(\pi nx\right)\right)dx$

Killing form on some Lie algebra $L$ is zero. Is $L$ necessarily nilpotent?

Find the Jordan normal form of a nilpotent matrix $N$ given the dimensions of the kernels of $N, N^2, N^3$

A finite field extension of $\mathbb R$ is either $\mathbb R$ or isomorphic to $\mathbb C$

$A$ is diagonalizable and $A^3 = A^2$

$f\colon(0,\infty)\to \mathbb R$ be continuous ; $f(x)\le f(nx) , \forall n \in \mathbb N , \forall x >0$ , then $\lim_{x\to \infty} f(x)$ exists?

A simple function equation

Can the limit $\lim_{h \to 0}\frac{f(x + h) - 2f(x) + f(x - h)}{h^2}$ exist if $f'(x)$ does not exist at $x$?

Show $\lim_{n_\rightarrow \infty}\int_0^\infty ne^{-\frac{2n^2x^2}{x + 1}}dx = \infty$

Find linear transformation given kernel

Topology that makes the finite set $X =\{1,2,3,4,5\}$ a regular space

The set of all limits of sub-series of an absolute convergent series

Grandi's series with 3 numbers

What is the value of $\lim _{x\to 0}\left\lfloor\frac{\tan x \sin x}{x^2}\right\rfloor$

Proof of minimum eigenvalue of non-symmetric matrix with real eigenvalues

When are these quotient rings isomorphic?

Composition of convex and power function

Chain rule question total differentiation

Divergence Theorem Question

Find all real and continuous functions that are a 3-involution.

Showing that a derivable function $f$ (satisfying some conditions) is null.

Pointwise and uniform convergence of sequence of functions