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Martin R
  • Member for 9 years, 9 months
  • Last seen this week
  • Germany
152 votes
Accepted

Why does this matrix give the derivative of a function?

76 votes

If a two variable smooth function has two global minima, will it necessarily have a third critical point?

64 votes
Accepted

Taylor series for $\sqrt{x}$?

28 votes
Accepted

What are the coefficients in the expansion of $(x+y)(x+2y) \cdots (x+ny)$?

26 votes
Accepted

Is the AM-GM inequality the only obstruction for getting a specific sum and product?

25 votes

How to prove that adding $n$ to the numerator and denominator will move the resultant fraction close to $1$?

21 votes

Are balls around a point always symmetric about the axes?

20 votes
Accepted

Pair of functions with same values and same derivatives at distinct points

19 votes
Accepted

Show that $f'(c) +9 \int_{0}^{1/3} f(x) \, dx = 0$ for some $c$ if $\int_{0}^{1} f(x) \, dx = 0$

19 votes

Show that $\int_{0}^{\pi/6} {\cos (x^2)}\mathrm{d}x\ge\frac12$.

18 votes
Accepted

Is $d(x,y)=\frac {\|x-y\|} {\sqrt {1+\|x\|^{2}}\sqrt {1+\|y\|^{2}}}$ a metric on a normed linear space?

16 votes
Accepted

Help to understand the generalization of the Argument Principle

16 votes
Accepted

Let $f:\mathbb{R} \to \mathbb{R}$ continuous with $f(f(x))=e^x$, show that $\lim_{x\to \infty } \frac{f(x)}{x^n}=\infty$ (Brazilian Olympiad)

15 votes
Accepted

A problem from the Shortlist of the Romanian Mathematics Olympiad

15 votes
Accepted

Prove that $\int_0^1 \big(1-x^2\big) \big(f'(x)\big)^2\,dx \ge 24 \left(\int_0^1 xf(x)\,dx\right)^{\!2}$

15 votes

Prove that $\det(A)=p_1p_2-ba={bf(a)-af(b)\over b-a}$

15 votes
Accepted

Pigeonhole Principle - Roulette Wheel

15 votes
Accepted

For f continuous on $[0,1]$, show that there exist points $\alpha_k$ such that $\sum \limits_{k=1}^n \frac{1}{f'(\alpha_k)} = n $

15 votes
Accepted

Find the number of roots of a polynomial using Rouche's Theorem

14 votes

An absolutely convergent series of rational numbers which does not converge to a rational number

14 votes
Accepted

Rolle's theorem $\beta \cdot f(x)+f'(x)=0$

13 votes
Accepted

When is composition of meromorphic functions meromorphic

13 votes
Accepted

Condition to guarantee $f=0$ on $[a,b]$

12 votes
Accepted

How to prove that $\lVert x + y\rVert = \lVert x\rVert + \lVert y \rVert \implies \lVert tx + (1-t)y\rVert = t\lVert x\rVert + (1-t)\lVert y \rVert$?

12 votes
Accepted

Entire functions such that $\frac{f(z+1)-f(z-1)}{2}=f'(z)$

12 votes
Accepted

The sum of square roots of non-perfect squares is never integer

12 votes
Accepted

Prove the roots of $z^7+7z^4+4z+1=0$ lie inside a circle of radius $2$.

12 votes
Accepted

Is it true that if $\limsup\limits_{n \to \infty}\left|\frac{a_{n+1}}{a_n}\right| > 1$, then $\sum a_n$ diverges?

11 votes
Accepted

Show that $f(z)=0$ for all $z$, where $f$ is an analytic function on the closed unit disc with additional conditions.

11 votes
Accepted

Alternative proof that if $a,b,c \in \mathbb{R}$ and $(a+b+c)c<0$ then $b^2-4ac>0$?

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