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Joe Shmo's user avatar
Joe Shmo's user avatar
Joe Shmo's user avatar
Joe Shmo
  • Member for 8 years, 9 months
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5 votes

Uniform convergence of $\{f_n\}$ satisfying $f_n\left(x + \frac{1}{n}\right) = f_n(x)$ implies that the limit is a constant function

3 votes
Accepted

What is the possible value of: $\frac{a}{b}+\frac{b}{a}-ab$

3 votes
Accepted

$\int_0^1|f(x)|dx=0$ if and only if $f(x)=0$ for all $x\in[0,1]$

3 votes
Accepted

Artin's Algebra $4.3.3$

3 votes
Accepted

How to show that $n^{-1}s_n \rightarrow 0$ if $n^{-2}s_{n^{2}} \rightarrow 0$?

3 votes

How to decide whether this series $\sum_{n=1}^\infty \dfrac{(-1)^n n^3+n^2}{n^4+1}$ is convergent or divergent

2 votes

Sum of 3 vectors is $\vec 0$

1 vote

Suppose that $a_n\neq0$ for all $n\in\mathbb{N}$ and $L=\lim_{n\rightarrow\infty}\left|\frac{a_{n+1}}{a_n}\right|$. Prove that $a_{n}\to 0$.

1 vote

Let $h$ be such that $h(x)=\int_a^x f'(t)dt$. For which value of $a$ is function $h$ identical to function $f$?

1 vote

Is every eigenvector of $T$ is also eigenvector of $g(T)?$

1 vote

Finding the limit $\lim_{x\to\infty}\left(1 + a^x\right)^{(1/x)}$ for $a > 0$

1 vote
Accepted

Is a bounded polynomial constant?

1 vote
Accepted

If $X \sim f(x)$ is symmetric then the median of X is $a$

1 vote

Is the integral $\int_0^T |f(x)| dx$ always strictly greater than $0$?

0 votes

Linear transformation $T$ that is diagonal with respect to every basis then $T$ has only one eigenvalue.

0 votes

Uniform convergence of $f_n(x) = \left(1 + \frac{x}{n}\right)^n$ when calculating limit

0 votes

Proof verification: Given $\lim_{x\to 0}\frac{f(2x)-f(x)}{x}=0$ and $\lim_{x\to 0} f(x)=0$, show that $\lim _{x\to 0}\frac {f(x)}{x}=0$.

0 votes

Given $a_{1} = \frac{1}{2},\;\;a_{n+1} = \frac{a_{n} +3}{4},\;\;n ≥ 1$, find $L = \lim_{n\to \infty} a_{n+1}$.

0 votes

If 2 spaces are homotopy equivalent, then their fundamental group is the same

0 votes

Find the infimum of the set $\{x+\frac 1x\}$

0 votes

Why is gradient the direction of steepest ascent?