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14
Is there a way to find this limit algebraically? $\lim\limits_{x\to \infty} \frac{x}{\sqrt{x^2 + 1}}$
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12
Prove that $\neg \exists x$ such that $ \lvert x-1\rvert+\lvert x+1 \rvert <1$
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10
Show that $\lim\limits_{(x,y)\to(0,0)}\frac{x^3y-xy^3}{x^4+2y^4}$ does not exist.
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10
Can a uncountable union of finite sets be uncountable?
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9
$x \cdot y$ is an integer and $x - y$ is an integer. Do $x$ and $y$ both have to be integers?
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8
$\int \frac{dx}{\sin x-\cos x}$
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7
$\int[\exp(\ j\cdot\phi\cdot x)\cdot \exp(j\cdot k\cdot x\cdot \sin \theta)] \mathrm dx$
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7
Evaluate $\int \frac{dx}{\left(\frac{1}{x}-\frac{1}{a}\right)}$
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7
How to prove $\big | e^{it}-1 \big |=2 \bigg |\sin \left(\frac{t}{2}\right) \bigg |$
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7
Are there any functions that are differentiable but not continuously-differentiable?
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7
Any smart approach to finding a matrix given the characteristic polynomial?
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7
If $1, \alpha _1,\ldots,\alpha _{n-1}$ are the roots of $x^n - 1 = 0$, then $n =(1-\alpha_1)(1-\alpha_2)\cdots(1-\alpha_{n-1}).$
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6
$x \mapsto x^n $ is a automorphism of group $G$, show that for all $x$ in $G$, $x^{n-1} \in Z(G)$.
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6
Connectedness in the Quotient Space
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6
Proving that $\Bbb Q^n$ is dense in $\Bbb R^n$
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6
Is it true that $f(X)$ is countable implies $f$ is measurable?
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6
Is weak convergence "limit" unique?
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6
If $f$ is a nonconstant entire function such that $|f(z)|\geq M|z|^n$ for $|z|\geq R$, then $f$ is a polynomial of degree atleast $n$.
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6
If ${\rm Im} (T) = \ker (T)$, then $T$ is nilpotent.
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6
Semisimple Rings are Noetherian
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5
Prove that $f(x) = \sum_{n=1}^{\infty} x^n/n^2$ is continuous on $[0,1]$
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5
An example of open but not closed map.
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5
Prove that there exists a polynomial in $\mathbb{Q}[x]$ with the root $2-\sqrt7$.
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5
Prove that $X/A \cong (\Bbb{R^*};.)$.
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5
Limit of $\frac{1}{7}e^{-2x^2}(1-4x^2)$ as $x\to\infty$
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5
Let $x=1+\frac{1}{2+\frac{1}{1+\frac{1}{2+\frac{1}{...}}}}$; then the value of $(2x-1)^2$ equals...
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5
How to find the limit $\lim_{x \to 0}\frac{\sin(6x)}{8x}$?
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5
Proof of associativity of semidirect product
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5
The integral that $\int_{0}^{\pi/2} \frac{x\sin x+2-2 \cos x}{2\sin x+x\cos x+x}\,\mathrm dx=\ln 2$
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5
Let $R$ be a ring, and $M,N$ are $R$-modules, and $I=Ann(N)$. If $I$ contains an $M$-regular element, then $\text{Hom}_{R}(N,M)=0$.
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