Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 89

Use linearisation of a certain function to approximate $sqrt[3]{30}$

Background Find the linearisation of the function $$f(x)=sqrt[3]{{{x^2}}}$$ at $$a = 27.$$ Then, use the linearisation to find $$sqrt[3]{30}$$ My work so far Applying the formula ...

Asked on 11/12/2021

3 answer

Solving for positive reals: $abcd=1$, $a+b+c+d=28$, $ac+bc+cd+da+ac+bd=82/3$

$$a,b,c,d in mathbb{R}^{+}$$ $$ a+b+c+d=28$$$$ ab+bc+cd+da+ac+bd=frac{82}{3} $$$$ abcd = 1 $$ One can also look for the roots of polynomial $$begin{align}f(x) &=...

Asked on 11/12/2021

5 answer

Let $G$ be a finite group such that if $A, Ble G$ then $ABle G$. Prove $G$ is a solvable.

Let $G$ be a finite group satisfying the following property: (*) If $A, B$ are subgroups of $G$ then $AB$ is a subgroup of $G$....

Asked on 11/12/2021

2 answer

Convergence of $e^{itH}$ as a sum for $H$ and unbounded operator

Let $H$ be an unbounded operator on a Hilbert space $mathcal{H}$. We may define the propagator $U(t)=e^{itH}$ via the functional calculus. However, if $H$ were bounded,...

Asked on 11/12/2021 by user293794

1 answer

Are final functors stable under pullback?

Recall the notion of a final functor, which is a sort of colimit-preservation property.Is such class of functors stable under pullbacks in Cat? Namely, is the...

Asked on 11/12/2021 by geodude

1 answer

Optimal location of nucleation sites for voronoi partition of a square

Do there exist algorithms to place n-points inside a square such that the Voronoi partition of the square (using these n-points as nucleation sites) minimizes the largest Voronoi cell in...

Asked on 11/12/2021 by Mouli

0 answer

If an element $cinmathbb{U}_m$ has order $o$, then $mathbb{U}_m$ has elements of every order less than $o$

I’m trying to prove that, if some $cinmathbb{U}_m$ has order $o$ (i.e. $c^o = 1$), $mathbb{U}_m$ contains elements of every order less than $o$. It...

Asked on 11/12/2021 by K_M

0 answer

Different ways for stating the recursion theorem

I've been trying to understand the recursion theorem for quite a while now and I still don't think I understand it 100%, I've checked multiple books and pdfs and I've...

Asked on 11/12/2021

2 answer

Example of a flow that does not preserve volume measure (autonomous ode)

Consider the autonomous differential equation in $mathcal{U} = mathbb{R} times (0, +infty)$ given by $$x' = dfrac{x^2}{1+x^2y^2}, y' = 0.$$ Justify that the respective flow is complete (i.é,...

Asked on 11/12/2021 by Raquel Magalhães

0 answer

Homomorphic Image of ideal in Lie algebras

I try to prove the following theorem which given without proof here On Prime Ideals of Lie AlgebrasTheorem: Let $L$ and $L^{prime}$ be Lie algebras...

Asked on 11/12/2021 by Hamada Al

1 answer

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