An elevator ride down Steven stories

opatovaL
2021-02-05
Answered

An elevator ride down Steven stories

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hosentak

Answered 2021-02-06
Author has **100** answers

Since the elevator is going down, the situation is represented by a negative integer. Since it goes down 7 stories, then it is represented by the integer −7.

asked 2021-04-06

Find the point on the plane $x+2y+3z=13$ that is closest to the point (1,1,1). How would you minimize the function?

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Find an equation of the tangent plane to the given surface at the specified point. $z=3{y}^{2}-2{x}^{2}+x,\text{}(2,-1,-3)$

asked 2020-11-07

Show that the least upper bound of a set of negative numbers cannot be positive.

asked 2021-06-13

A set of ordered pairs is called a _______.

asked 2022-04-12

Prove that for every natural number n, fraction $\frac{21n+4}{14n+3}$ is irreducible. I deduced that if we can prove that numerator and denominator have 1 as their GCD, we can get the result, but I cannot get it from thereon.

asked 2022-05-13

Let ${\left\{{f}_{k}\right\}}_{k=1}^{\mathrm{\infty}}$ be a sequence of $\mathcal{S}$-measurable real-valued functions on a measure space $(M,\mathcal{S})$. Then the functions

$\underset{k\to \mathrm{\infty}}{lim\u2006sup}{f}_{k}(x)\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\underset{k\to \mathrm{\infty}}{lim\u2006inf}{f}_{k}(x)$

are also $\mathcal{S}$-measurable.

I already have proven this statement and my question is about something else. In the script it says that the reader may use the hint:

For a sequence ${\left\{{a}_{k}\right\}}_{k=1}^{\mathrm{\infty}}$ of real numbers the following is true:

$\underset{k\to \mathrm{\infty}}{lim\u2006sup}{a}_{k}=\underset{k\to \mathrm{\infty}}{lim}\underset{m\to \mathrm{\infty}}{lim}max\{{a}_{k},{a}_{k+1},\dots ,{a}_{m}\}$

Now, I have not used this in my proof, but I can assure you, that my proof is airtight nonetheless. Anyway, can someone point out why this holds? I have not seen this equality before and did not know that one can present $lim\u2006sup,lim\u2006inf$ like that. I know that for a set of limit points $H$ we can say that $lim\u2006supH=maxH$ and vice versa. I do not even see how this property can be useful for our proof.

$\underset{k\to \mathrm{\infty}}{lim\u2006sup}{f}_{k}(x)\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\underset{k\to \mathrm{\infty}}{lim\u2006inf}{f}_{k}(x)$

are also $\mathcal{S}$-measurable.

I already have proven this statement and my question is about something else. In the script it says that the reader may use the hint:

For a sequence ${\left\{{a}_{k}\right\}}_{k=1}^{\mathrm{\infty}}$ of real numbers the following is true:

$\underset{k\to \mathrm{\infty}}{lim\u2006sup}{a}_{k}=\underset{k\to \mathrm{\infty}}{lim}\underset{m\to \mathrm{\infty}}{lim}max\{{a}_{k},{a}_{k+1},\dots ,{a}_{m}\}$

Now, I have not used this in my proof, but I can assure you, that my proof is airtight nonetheless. Anyway, can someone point out why this holds? I have not seen this equality before and did not know that one can present $lim\u2006sup,lim\u2006inf$ like that. I know that for a set of limit points $H$ we can say that $lim\u2006supH=maxH$ and vice versa. I do not even see how this property can be useful for our proof.

asked 2022-08-06

Simplify. $\frac{2n!}{(n-1)!n!{4}^{n}}$