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Jungleshrimp's user avatar
Jungleshrimp
  • Member for 6 years, 6 months
  • Last seen more than a week ago
8 votes
2 answers
455 views

Finite groups $A$ and $B$. Does existence of surjective group homomorphism $f:A\to B$ imply existence of an injective homomorphism $g:B\to A$?

6 votes
6 answers
188 views

Assume that $\int_{a}^{ab} f(x) dx$ is independent of $a$. Prove $f(x)=\frac{c}{x}$

5 votes
2 answers
1k views

Why does a power series converge absolutely within the radius of convergence using the root test?

5 votes
2 answers
79 views

Existence of homomorphism $\phi:\mathbb{Z}[[X]]\to\mathbb{Q}$ such that $\phi(X)=3/4$?

5 votes
1 answer
255 views

If a function $f$ is Riemann integrable on $[a,b]$, then how do I know $\lim_{N\to\infty}\sum_{n=1}^{N} f(x_n)\frac{b-a}{n}$ gives the right answer?

5 votes
1 answer
80 views

Evaluating a limit where the ratio test fails $\lim_{n\to\infty} \frac{1}{2^{2n}}\frac{(2n)!}{(n!)^2}\sqrt{n}$. [closed]

4 votes
1 answer
77 views

Proving the index of a subgroup

4 votes
2 answers
205 views

$\mathbb{R}$ with the right topology is pseudocompact.

4 votes
1 answer
226 views

Topology GRE-esque question

4 votes
3 answers
612 views

How do I perform a change of variables with a monotonically decreasing function?

3 votes
2 answers
128 views

Convergence of the series $\sum_{n=1}^\infty [\frac{1}{\sqrt{n}}-\sqrt{\ln(1+\frac{1}{n})}]$.

3 votes
1 answer
2k views

Inner product proof involving one-to-one linear transformations.

2 votes
3 answers
4k views

Show that the set $\{(x,y): xy=1, x>0\}$ is closed

2 votes
0 answers
240 views

Proof that $\lim_{n\to\infty} \frac{1}{x_n}$= $\frac{1}{L}$

2 votes
1 answer
166 views

How can I compare two series that are same thing, but at different rates?

2 votes
2 answers
2k views

A closed bounded set contains its supremum

2 votes
1 answer
194 views

$DF(a)$ is invertible and $F(a)=0$. Imply $C^1$?

2 votes
1 answer
39 views

Finding the limit $\lim_{x\to\infty} (x^3-x^2+\frac{x}{2})e^\frac{1}{x} -\sqrt{x^6+1}$

2 votes
1 answer
60 views

Suppose $\{a_n\}_{n=1}^{\infty}$ is a bounded. Suppose $\lim_{n\to\infty} (a_{2n}+2a_n)=0$. Prove that $\lim_{n\to\infty} a_n=0$ [duplicate]

2 votes
1 answer
239 views

Which of the following is closest to the value of the integral $\int_0^1 \sqrt{1+\frac{1}{3x}} dx$?

2 votes
1 answer
5k views

Fourier coefficients of $x(\pi-x)$ on $(0,\pi)$

2 votes
1 answer
800 views

Convergence of the series $\sum_{n\neq0} \frac{e^{inx}}{n}$ Using Dirichlet's test.

2 votes
2 answers
210 views

$|e^{-ina}-e^{-inb}|=2\sin(n\theta_0)$

2 votes
2 answers
111 views

Solutions to $\int\limits_x^{x^2} f(t)\ dt=\int\limits_1^x f(t)\ dt$? [duplicate]

2 votes
1 answer
51 views

Divergence of the series $\sum x_n$ with terms satisfying $\frac{x_{n+1}}{x_n}>1-\frac{1}{n}$ for all $n\in\mathbb{N}$

2 votes
1 answer
108 views

If $\int_{0}^{1} f(x)x^n dx=0$ for $n=0,1,2,3,...$, then $f=0$ on $[0,1]$

2 votes
0 answers
41 views

How to equip $\frac{\mathbb{Z}}{5\mathbb{Z}}$ with the structure of a $(\frac{\mathbb{Z}}{5\mathbb{Z}}[x])/(x^2+1)$-module?

2 votes
0 answers
20 views

Uniqueness of limit points of a gradient equation $u'+\nabla_u f(u)=0$ in one dimension

2 votes
0 answers
49 views

What regularity guarantees existence of solutions to the Dirichlet problem for the Laplace equation?

1 vote
2 answers
58 views

Let $p$ be prime. What is the biggest number $m$ such that $\{1,\zeta_p,\zeta_p^2,...,\zeta_p^m\}$ is linearly independent over $\mathbb{Q}$?