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Mathematics : Recent Questions and Answers (Page 29)

Find answers to your questions about Mathematics or help others by answering their Mathematics questions.

How does the process of simplifying imaginary numbers actually work?

Sorry in advance if this is a really stupid questionIn class I've been told that $$sqrt{-25} = 5j $$Converting $sqrt{-25} $ into $5j$ is straightforward...

Asked on 12/20/2021

5 answer

Finding the height of a Pyramid where the sides are given by an equation

Problem: The vertex of a pyramid lies at the origin, and the base is perpendicular to the x-axis at $x = 4$. The cross sections of the pyramid perpendicular...

Asked on 12/20/2021

2 answer

L'hopital rule fails with limits to infinity?

$$ lim_{n to infty} frac{1 +cn^2}{(2n+3 + 2 sin n)^2} = ? $$ if I factor the $n^2$ out of denominator, $$ lim_{n to infty}...

Asked on 12/20/2021

1 answer

Linear programming with min of max function

I have to write the linear program which minimizes this function : $$y = max_j sum_{i=1}^{n}c_{ij}x_{ij}$$ My book says that this is not a linear function but it can...

Asked on 12/20/2021

2 answer

How should one understand the "indefinite integral" notation $int f(x);dx$ in calculus?

In calculus, it is said that $$int f(x); dx=F(x)quadtext{means}quad F'(x)=f(x)tag{1}$$where $F$ is a differentiable function on some open integral $I$. But the mean...

Asked on 12/20/2021 by user9464

5 answer

Zeros and poles of rational function.

Suppose we are given a rational function$$f(s) = frac{25s}{s^4+18s^3 +134s^2 +472s+680} $$ and we need to find the zeros and poles of the function. Suppose $f(s) =...

Asked on 12/20/2021

1 answer

I need to help with a formula to find the length of a line.

I have a rectangle which I know the width and height of it.I need to draw a line inside the rectangle and the information that I have include knowing...

Asked on 12/20/2021 by user3762238

2 answer

Sequence of Lebesgue integrable functions bounded in norm converges pointwise

I've come across a problem which states: Given a sequence of integrable functions ${f_k}$ ($k≥1$) on $[0,1]$ with the property that $||f_k||_1 ≤ frac{1}{2^k} $,...

Asked on 12/20/2021

1 answer

Let $Lambda(x)=(lambda_1x_1,lambda_2x_n,...)$ be an operator $l_2 to l_2$. Show its range is closed iff $inf_{lambda_knot=0} |lambda_k|>0$

Let $Lambda(x)=(lambda_1x_1,lambda_2x_n,...)$ be an operator $l_2 to l_2$. Show its range is closed iff $inf_{lambda_knot=0} |lambda_k|>0$. I proved the backwards direction. If $x_n$ is Cauchy in...

Asked on 12/20/2021

1 answer

Name for "orthogonal eigenvalues" of a matrix

It seems that any $ntimes n$ matrix $A$ can be written like $QLambda O^T$ for orthogonal matrices $Q,O$ and diagonal matrix $Lambda$. I want to...

Asked on 12/20/2021 by Marcus Luebke

0 answer

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