# 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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### Expanding random N(0,1) variable

If I have an expression $$\frac{1}{1+\sigma m(z/l)}$$ where $m(z/l)$ is a random $N(0,1)$ variable, $\sigma$ is dimensionless, can I rewrite this via an expansion to bring up the random variable on ...
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### Proving limit of f(x) - Tnf(x) (Taylor) is zero, in multivariable calculus

So as we all probably know, for $f : \mathbb{R} \to \mathbb{R}$, and $T_nf(x)$ the taylor polynomial at a given point a, we have $\lim\limits_{x \to a} \frac{f(x) - T_nf(x)}{(x-a)^n} = 0$. Our ...
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### Stuck trying to find the value of this limit using Taylor series.

So I'm having trouble trying to find the value of the limit $$\lim_{x \to 0}\frac{(\sqrt{2}-\sqrt{1+\cos(x)})(e^x-e^{-x})}{\sin^3(x)}$$ using Taylor series (the problem explicits it). Well, this is ...
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### Taylor series and calculating a sum with its help

So this function is given: $$f(x)=xe^{-2x}$$ I have to calculate its Taylor series around $x=1$ and use it in some way to calculate the following sum: $$\sum_{n=1}^{\infty} \frac{n+2}{(2n)!!}$$ I ...
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### Lagrange remainder - is t contained within an open or closed interval?

Above is the taylor series centred at a including the lagrange remainder. Can t be equal to a or b?
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### Asymptotic expansion of integral - issue with step in proof

I have been trying to read Asymptotic Analysis by J.D Murray. There is a page in the book, rather, a certain line in this page, that has confused me thoroughly. What was said on the page before, is ...
The question asks: Let $f:\mathbb{R}\longrightarrow\mathbb{R}$ be defined by $f(x)=e^x$ (a) Find the $n$th order Taylor polynomial about x = 0, and the corresponding remainder term. I can quite ...