Ben Martin's user avatar
Ben Martin's user avatar
Ben Martin's user avatar
Ben Martin
  • Member for 7 years
  • Last seen this week
7 votes

Minimum value of $(x^2+y^2)^2$

6 votes
Accepted

Prove combinatorially that: $\displaystyle {{n}\choose{k}} {{n}\choose{m}} = \sum^{k}_{i=0} {{n}\choose{m+i}}{{m+i}\choose{k}} {{k}\choose{i}}$

4 votes
Accepted

What is the limit $a_{n+1}=\frac{1+c_n}{1+\frac{1}{b_n}}$ when n goes to infinity?

4 votes
Accepted

Function equal its integral implies zero function

4 votes
Accepted

Expectation of Spherically Symmetric Random Vector

4 votes
Accepted

Proof that sum of k-eigenvalues is convex

3 votes
Accepted

A weak condition for normality of a subgroup.

3 votes
Accepted

Can one compute 'double' (or even triple) simultaneous derivatives: $\frac{F(x+dx,y+dy)-F(x,y)}{dxdy}$

3 votes
Accepted

Multiplication of Infinity

3 votes

Surprising appearance of triangular numbers during simple coin flip game

2 votes

A natural number $n$ is called "good" when it is equal to multiplying two consecutive natural numbers . Is there ...

2 votes
Accepted

Proof that solutions of the ODE $y''+q(x)y=0$ have at least one zero

2 votes

Let $f$ continous and satisfies that $\int_{0}^{x^2}f(t) dt= x^2(x+1)$ calculate f(2)

2 votes
Accepted

How to prove that $\exists \xi\in[a,b],f(\xi)=g(\xi)$

2 votes
Accepted

Prove or disprove: there exists no binary operation $*$ on $\mathbb Q^+$ s.t. $(\mathbb Q^+,*)$ is not isomorphic to $(\mathbb Q^+,×)$

2 votes
Accepted

Find $\lim \limits_{x\to 0} \frac{\sin({\pi \sqrt{\cos x})}}{x} $

2 votes
Accepted

Difference quotients and Lipschitz

2 votes

Method of characteristics and $\partial_x F(x,\phi(x)) = \partial_y F(x,\phi(x)) = 0$.

2 votes

General Solution of $|z-a| + |z-b| = c$

2 votes

How to obtain the asymptote formula of $\int_{0}^{\pi/2}\sqrt[n]{\cos x}\,dx$?

2 votes
Accepted

Proof that expectation of $X^T \Sigma^{-1} X = \dim X$

2 votes
Accepted

converting range constraint into a domain constraint for parametric surface

2 votes
Accepted

How to evaluate the integral $\int_{1}^{e} \frac{\ln(x)}{\left( 1+\ln(x) \right)^2}dx$?

2 votes
Accepted

How to compute $\int_{a}^{b}\sqrt{\mathrm dx}$

1 vote

Solve the initial value problem with 4 conditions.

1 vote

$||y|-1|>2$ inequality

1 vote

What is the method to solve $\min(5-15a-18b+15a^2+45ab+45b^2)$

1 vote
Accepted

convergence radius of two specific power series

1 vote
Accepted

Calculate an integral $\int_0^1 t^\frac{1}{z}(1-\ln t^\frac{1}{z})dz$

1 vote
Accepted

Let $f(x)$ be a smooth function. What is the geometric intuition for why $\int_{0}^{2\pi}f(x)\sin(nx) < \int_{0}^{2\pi}f(x)\sin(mx)$ for $n<m$?