# Questions tagged [analysis]

Mathematical analysis. Consider a more specific tag instead: (real-analysis), (complex-analysis), (functional-analysis), (fourier-analysis), (measure-theory), (calculus-of-variations), etc. For data analysis, use (data-analysis).

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### Determinate $d^{k}f_{c}$ for function $f(x,y)$ with k and c given

In my Calculus 3 class I have been given following problem: Determinate: $d^{k}f_{c}$ for function $f(x,y)$ where $c = (c1,c2)$ and $k = 2$. My problem is that I have no clue what does $d^{k}f_{c}$ ...
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### Evaluating the value of |$f'(x)$| [duplicate]

Let $f \in C^2[0,2]$ and $|f(x)| \le 1, |f''(x)|\le1$ for all $x \in[0,1]$ Prove that $|f'(x)|\le2$ for all $x \in [0,2]$ I tried Taylor expansion to evaluate $|f'(x)|$, but it seems to work only ...
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### Is the convolution of $L^2$ functions continuous? [duplicate]

Is the answer to the following question positive? The convolution of two $L^2(\mathbb R)$ functions is continuous I briefly recall it here: Take $f$ and $g$ $\in L^2(\mathbb R)$, then I want to show ...
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1 vote
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### Explanation about this probabilistic proof that leads to $log_RN$

I am reading a proof based on (probabilistic) analysis on how a specific data structure performs for the case of search miss. The base assumption is that the probability that each of the $N$ keys in a ...
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### Extrapolate impression values from total impressions.

Im looking to extrapolate impression values for specific page level URLs however I only have the total impressions for a domain, and the ranking of the URLs (where the closer you are to 1 the higher ...
1 vote
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### Understanding Real analyticity

I'm going to state my assumption of the definition of Real analyticity, and how I understand it based on my current understanding. Please tell me if they are correct or not and please help me ...
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### Is a continuous function on compact convex set where the boundary is mapped to the set a self mapping?

Let $K ⊂ R^n$ be convex and compact with $0$ in the interior of $K$. Let $f ∈ C(K, R^n)$ with $f(∂K) ⊂ K$. If this is the case, do we in fact have $f(K) \subset K$. It is probably not the case that ...
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### What does "contained continuously" mean? As in, "metric space $X$ is contained continuously in metric space $Y$".

What we mean by the "Contained continuously" terminology?! Definition: Let $H$ be a Hilbert space and $E$ is an open bounded subset of $\mathbb[C]$. The Hilbert space of measurable ...
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