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calculus question related to derivative of an integral [closed]

let g be differentiable function at [-1,1], such that g(0) = 0 and g'(0) = 1 does the next limit exists? and if so, what is it? https://i.imgsafe.org/b9fe48f29b.png I understand I need to use l'...
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An answer to this system of PDE's

Planning of the question: Let $(M,g)$ be a Riemannian manifold and $TM$ be its tangent bundle The isotropic almost complex structures $J_{\delta , \sigma}$ were introduced by Aguilar on the ...
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Creating a model based on info, calculus [closed]

A town's rate of population change is modeled by P'(t) = 34t + 16, where t is number of years since 1990 an P'(t) is in people per years. a) Find the population model for this town if it is known ...
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Finiteness / convergence of differential extensions [closed]

The topic of this question is the integration of symbolic expressions: integration in finite terms. It was introduced by Liouville. I want to help to answer "Generalization of Liouville's Theorem" in ...
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Approximate largest eigenvalue of Monodromy matrix

Does anyone know the procedure (or have pseudo code) to approximating the largest eigenvalue of a monodromy matrix? Or even to approximate the monodromy matrix itself? There is no explicit solution ...
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Computing skewness derivative in terms of variance

In the Portilla Simoncelli paper (page 18): http://www.cns.nyu.edu/pub/lcv/portilla99-reprint.pdf They go about calculating the derivative of the skewness $\eta(x)$ of a distribution (2D matrix in ...
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Is first term of my cost function convex?

I have an optimization problem in the form of [\begin{array}{l} \mathop {{\rm{Minimize}}}\limits_{\bf{X}} \,\,\,2\left| \delta \right|\sqrt {{\rm{Tr}}\left( {{\bf{A}}{{\bf{X}}^2}} \right)} {\rm{ - ...
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Boundary of an open, bounded and convex set in $\mathbb{R} ^n$

Let $U$ be an open, bounded and convex set in $\mathbb{R} ^n$. Since $\partial U$ is a rectifiable set it follows that up to a set of $H^{n-1}$-measure zero $\partial U$ is contained in a countable ...
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Looking for author of calculus quote

When I was a lowly calculus student many many years ago, my calculus teacher quoted some famous mathemtician: "Calculus is the last course in arithmetic and the first course in mathematics that one ...
Let $p(x_{1},x_{2},\ldots,x_{n})=\sum_{i,j=1}^{n}{a_{ij}x_{i}x_{j}}$ be a homogenous multivariate polynomial of degree $2$. I would like to know how many extrema $p$ has on the standard simplex ...