# All Questions

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### Partition a set of m objects into n subsets of positive size and no two of them should have equal size.

In how many ways can I partition a set of size m into n subsets such that each of them must have atleast one element and no two of them should have same no. of elements. ?
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### Find circle from normal vector and second point

I'm given two points on a circle: a point $(x_1, y_1)$ with corresponding normal vector $(u_1, v_1)$ and a second point $(x_2, y_2)$ (without normal vector). How can I compute the circle? ...
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### Limits, Determinants and Inversion of a matrix-valued function

Suppose I have a matrix-valued, continuous function $$A\colon [0,\infty) \to \mathbb R^{n\times n},\qquad h\mapsto A(h).$$ I know that for the limit $h\to 0$ the matrix is invertible: ...
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### If X ∼ N(µ, σ2 ) find the pdf of Y = e ^ X.

Help? I am stuck on this homework question and finding very difficult to answer
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### Unique periodic orbit for ODE consequence of Poincaré–Bendixson and Dulac’s Criterion

The Chicone exercise 1.201 asks prove that the system $$\dot x=x+y-x^3=g(x,y)$$ $$\dot y=x-y-y^3=h(x,y)$$ has a unique globally attracting limit cycle on the punctured plane. I prove that if exist a ...
### How to show that for the Schläfli symbol$\{m,k\}$ the polygon is non-degenerate if $m$ and $k$ are coprime?
I know by definition that if the elements of the Schläfli symbol $\{m,k\}$ are coprime then the polygon is non-degenerate, i.e. can be traced without lifting a pencil off of the paper. Is it possible ...
### Convergence of improper integral $\int_0^\infty x^{\alpha +1} e^{-x} dx$
Determine the convergence of the following improper integral as $\alpha \in \mathbb{R}$ varies: $\int_0^\infty x^{\alpha +1} e^{-x} dx$ I tried to do it in this way $e^{-x}<\frac{1}{x^{\beta}}$ ...