# All Questions

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### Proving that $\exists f: \mathbb{D}\to\mathbb{D}$, biholomorphic, which maps $z_1$ to $w_1$

Consider a pair of points, $z_1, w_1 \in \mathbb{D}$, where $\mathbb{D}$ is the unit disc centred at the origin. Is it sufficient to argue that $f(z)=z+a$ (for $a\in \mathbb{C}$) is biholomorphic, ...
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### Convention on Cauchy's two line notation for permutations

Let $n\in\mathbb{N}$. A permutation $\sigma\in S_n$ is denoted in Cauchy's two line notation as follow: \begin{pmatrix} 1 & 2 & \cdots & n \\ \sigma(1) & \sigma(2) & \cdots & \...
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### Parametric Equation part A

Hi everyone I am in need of some guidance solving this parametric equation question and was wondering if you guys could give me some pointers and to see if I am doing this correctly. Here I have two ...
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### Evaluate $\lim_{x\to 0} \frac{1}{x^3}\int_{0}^{x} \sin^{2}(3t)dt$

$$\lim_{x\to 0} \frac{1}{x^3}\int_{0}^{x} \sin^{2}(3t)dt$$ $$\lim_{x\to 0} \frac{1}{x^3}\int_{0}^{x} \sin^{2}(3t)dt=\lim_{x\to 0} \frac{\int_{0}^{x} \sin^{2}(3t)dt}{{x^3}}$$ I know that the limit ...
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### Term for a function that is an involution on its image

Is there a specific term for a function $f:X\to X$ that obeys the law $f^3(x)=f(x)$? It's not necessarily an involution, but it is an involution when its domain is restricted to its image. A simple ...

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