User Umberto P. - Mathematics Stack Exchange

56 votes

Does L'Hôpital's work the other way?

answered Nov 22, 2013 at 21:24

38 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?

answered Jan 22, 2018 at 15:50

36 votes

Trouble understanding only one way implication truth

answered Feb 5, 2018 at 20:52

28 votes

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

answered Oct 26, 2018 at 17:50

28 votes

Sum of reciprocal of primes

answered Aug 16, 2016 at 16:39

27 votes

Unique weak solution to the biharmonic equation

answered Sep 19, 2014 at 15:44

22 votes

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

answered Apr 17, 2017 at 14:01

20 votes

Accepted

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

answered Aug 19, 2016 at 19:57

18 votes

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

answered Oct 3, 2013 at 14:53

18 votes

Accepted

Image of open set is not open?

answered Dec 19, 2014 at 17:48

18 votes

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

answered Feb 6, 2015 at 18:11

16 votes

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

answered Mar 11, 2015 at 13:24

16 votes

Accepted

The proof of Morrey's Inequality in Evans Book

answered Dec 6, 2013 at 14:54

15 votes

Product of logarithms, prove this identity.

answered Mar 21, 2014 at 13:19

15 votes

Prove that $371\cdots 1$ is not prime

answered Apr 28, 2015 at 17:32

15 votes

Accepted

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

answered Aug 30, 2016 at 15:08

14 votes

Why can we interchange summations?

answered Aug 13, 2013 at 17:50

14 votes

Mistake in integration by parts

answered Nov 16, 2015 at 15:24

14 votes

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

answered Apr 19, 2017 at 15:06

13 votes

Is a constant as a function continuously differentiable?

answered Sep 16, 2013 at 18:15

13 votes

Accepted

Poisson's equation with Robin boundary conditions

answered Feb 1, 2015 at 15:00

13 votes

Accepted

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

answered Jan 1, 2015 at 22:02

13 votes

Accepted

prove that integral over set of small measure is small

answered Aug 26, 2016 at 17:53

12 votes

Accepted

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

answered Jan 22, 2015 at 15:57

12 votes

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

answered Dec 8, 2014 at 15:03

12 votes

Accepted

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

answered Jun 20, 2013 at 18:33

11 votes

A basis of a subspace is subset of a basis of the whole space

answered Apr 24, 2014 at 13:25

11 votes

Accepted

Why $2x$? Can't it be $x$?

answered Jul 3, 2014 at 16:25

11 votes

Accepted

Limit of this recursive sequence and convergence

answered Sep 5, 2014 at 18:02

11 votes

Accepted

Find a space whose dual does not separate points

answered Oct 2, 2014 at 20:22

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1,694 Answers

Does L'Hôpital's work the other way?

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

Trouble understanding only one way implication truth

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

Sum of reciprocal of primes

Unique weak solution to the biharmonic equation

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

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

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

Image of open set is not open?

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

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

The proof of Morrey's Inequality in Evans Book

Product of logarithms, prove this identity.

Prove that $371\cdots 1$ is not prime

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

Why can we interchange summations?

Mistake in integration by parts

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

Is a constant as a function continuously differentiable?

Poisson's equation with Robin boundary conditions

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

prove that integral over set of small measure is small

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

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

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

A basis of a subspace is subset of a basis of the whole space

Why $2x$? Can't it be $x$?

Limit of this recursive sequence and convergence

Find a space whose dual does not separate points