# Recent Questions (Page 4)

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## Prove that the functional in $C_c^0(Omega)$ is a Radon measure

Let $Omega subset mathbb{R}^n$ be an arbitrary open set and $(x_n)_{n inmathbb{N}} subset Omega$ a sequence. Let $(a_n)_{n inmathbb{N}} subset mathbb{C}$ be a sequence such that...

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Mathematics Asked on 1 year ago

## How can I evaluate ${lim_{hto 0}frac{cos(pi + h) + 1}{h}}$?

I'm supposed to evaluate the following limit using the cosine of a sum and one of the "special limits" which are ${lim_{xto 0}frac{sin(x)}{x}=1}$ and ${lim_{xto 0}frac{1-cos(x)}{x}=0}$. The limit...

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Mathematics Asked by DCdaKING on 1 year ago

## Estimate $f(b)$ using Taylor Expansion for $f'(x) = cos(x^2)$

I am using Taylor Expansion for the following problem, but for some reason I am getting wrong solutions from a program I am running it on. Can someone please help...

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Mathematics Asked by brucemcmc on 1 year ago

## If $f ∈ C^∞(M)$ has vanishing first-order Taylor polynomial at $p$, is it a finite sum of $gh$ for $g, h ∈ C^∞(M)$ that vanish at $p$?

This is 11-4(a) in Lee's "Introduction to Smooth Manifolds": Let $M$ be a smooth manifold with or without boundary and $p$ be a point of $M$. Let...

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Mathematics Asked by Fred Akalin on 1 year ago

$$sum_{n=1}^infty csc^2(omegapi n)= frac{A}{pi} +B$$ if $omega =-frac{1}{2}+frac{sqrt{3}}{2}i$ find $frac{A^2}{B^2}$My Attempt$$sum_{n=1}^infty csc^2(omegapi n)= sum_{n=1}^infty csch^2(iomegapi n)= 4sum_{n=1}^infty big(e^{pi n big( frac{i}{2} +... 2 Mathematics Asked by hwood87 on 1 year ago ## Show that f is a strong contraction when f is continuously differentiable. Let f: [a,b] to R be a differentiable function of one variable such that |f'(x)| le 1 for all xin [a,b]. Prove that f is a... 2 Mathematics Asked on 1 year ago ## Decomposition of a linear operator to a partially orthogonal operator and a semi-definite self-adjoint operator DeclareMathOperator{A}{mathscr{A}}$$DeclareMathOperator{B}{mathscr{B}}$$DeclareMathOperator{C}{mathscr{C}}$$DeclareMathOperator{kernel}{mathrm{Ker}}$$DeclareMathOperator{diag}{mathrm{diag}}$$DeclareMathOperator{span}{mathrm{span}}$$DeclareMathOperator{real}{mathbb{R}^2}$$DeclareMathOperator{rank}{text{rank}}$The question is:Let$A$be a linear operator on the$n$-dimensional Euclidean... 1 Mathematics Asked by Zhanxiong on 1 year ago ## Fourier expansions of Eisenstein series as a Poincare series for the Fuchsian group In Miyake's book, Modular Forms, Ch 2.6, thm 2.6.9, there is a statement which relate to Fourier expansion of the Eisenstein series. Let$Gamma$be a Fuchsian group, ... 1 Mathematics Asked by LWW on 1 year ago ## Is eigenvalue multiplied by constant also an eigenvalue? Let$A$be an$n × n$matrix. If$lambda$is an eigenvalue of$A$and$c$is a nonzero scalar, then$clambda$is... 1 Mathematics Asked by Ruby Cho on 1 year ago ## Can someone explain the proof of the following linear differential equation I was working through a robotics book, and came across the following equation, solution, and proof where$A$is a$n times n$constant matrix, and$x_0...

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Mathematics Asked by Lucas G on 1 year ago