# Questions tagged [taylor-expansion]

Questions regarding the Taylor series expansion of univariate and multivariate functions, including coefficients and bounds on remainders. A special case is also known as the Maclaurin series.

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### Singularities of $f(x)=\left(\sqrt{x+1}-\sqrt{x}\right)^{\alpha}$

I'm working with the following function $$f(x)=\left(\sqrt{x+1}-\sqrt{x}\right)^{\alpha}=\left(\frac{1}{\sqrt{x+1}+\sqrt{x}}\right)^{\alpha}$$ with $x\in[0,\infty)$ and $\alpha\in\mathbb{R}$. More ...
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### theorem on power series $\log(z^2-iz+2)$

I know how to solve this question.. but dont know using the theorem I know how to find radius of convergence as the wolframalpha says no poles for the log function, how to find then minimum distance ...
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### Best bound for the remainder of two variables Taylor's theorem

Let $f:\mathbb{R}^2 \to\mathbb{R}$ be a two times differentiable function. Then Taylor theorem says that there exists $t\in [0,1]$ such that \begin{align*} f({\bf x})=f({\bf a})+\sum_{i=1}^{2}\frac{\...
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