Umberto P.'s user avatar
Umberto P.'s user avatar
Umberto P.'s user avatar
Umberto P.
  • Member for 10 years, 11 months
  • Last seen this week
53 votes

Does L'Hôpital's work the other way?

36 votes

Trouble understanding only one way implication truth

35 votes
Accepted

If a compact set is covered by a finite union of open balls of same radii, can we always get a lesser radius?

28 votes

Sum of reciprocal of primes

28 votes

Is $\int_{\sin x}^{\cos x}x\, dx$ not a well-defined integral?

26 votes

Unique weak solution to the biharmonic equation

22 votes

Evaluate $\lim_{x\to 0} \frac{a^x -1}{x}$ without applying L'Hopital's Rule.

20 votes
Accepted

About absolute continuity $\Rightarrow$ null set maps to null set

18 votes

For every $\epsilon>0$ there exists $\delta>0$ such that $\int_A|f(x)|\mu(dx) < \epsilon$ whenever $\mu(A) < \delta$

18 votes

If $x \in\mathbb{Z}$ has the property that for all $m \in\mathbb Z$, $mx = m$, then $x = 1$

17 votes
Accepted

Image of open set is not open?

16 votes

How to explain the formula for the sum of a geometric series without calculus?

15 votes

Prove that $371\cdots 1$ is not prime

15 votes
Accepted

The proof of Morrey's Inequality in Evans Book

15 votes

Product of logarithms, prove this identity.

15 votes
Accepted

Prove this limit without using these techniques, and for beginner students: $\lim_{x\to0} \frac{e^x-1-x}{x^2}=\frac12$

14 votes

Does $\sum_{n=1}^\infty \frac{1}{\log(e^{n}+e^{-n})}$ converge or diverge?

14 votes

Mistake in integration by parts

13 votes
Accepted

prove that integral over set of small measure is small

13 votes

Why can we interchange summations?

12 votes

Is a constant as a function continuously differentiable?

12 votes
Accepted

Is $e^z + \overline{z}^2$ holomorphic?

12 votes
Accepted

Blackwell's condition for a contraction: Why is boundedness neccessary?

12 votes

An example of non-closed subspace of a Hilbert space?

11 votes
Accepted

Find a space whose dual does not separate points

11 votes

Why is the outer measure of the set of irrational numbers in the interval [0,1] equal to 1?

11 votes
Accepted

Sum of slowly varying functions

11 votes
Accepted

factor the following expression $25x^2 +5xy -6y^2$

11 votes
Accepted

Find $\lim_\limits{n\to \infty}\{en!\}$.

11 votes
Accepted

Evaluation of $\int_{-\pi}^{\pi}\sum_{r=0}^{2015}\cos (rx)\cdot \sum_{r=0}^{2015}\sin (rx)dx$

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