Choose 2 numbers from 100 numbers
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Choose 2 numbers from 100 numbers

If I want to choose a set of 2 positive integers less than 100, is that a permutation or a combination? I can't understand does the order matter in t...

Published: Aug 12, 2026

Forming a basis of P3(R) from a set S.
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Forming a basis of P3(R) from a set S.

I seem to have a good understanding of spanning sets and linear independence which then becomes essential for understanding basis, but I am unsure how all...

Published: Aug 12, 2026

Limit Proof of $e^x/x^n$ [duplicate]
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Limit Proof of $e^x/x^n$ [duplicate]

I am wondering how to prove $$\lim_{x\to \infty} \frac{e^x}{x^n}=\infty$$ I was thinking of using L'Hospital's rule? But then not sure how to do...

Published: Aug 12, 2026

What is the intuitive meaning of the adjugate matrix?
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What is the intuitive meaning of the adjugate matrix?

The definition of the adjugate matrix is easy to understand, but I have never seen it used for anything. What is the intuitive meaning of this matrix? Are...

Published: Aug 12, 2026

$n$th derivative of $\tanh$
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$n$th derivative of $\tanh$

Successive derivative of $\tanh u$ can be expressed as polynomial functions of $\tanh u$: \begin{align} \frac{d}{du}\tanh u&=1-\tanh^2u\\ \frac{d^2}{d...

Published: Aug 12, 2026

Which methods can be used to evaluate the following integral?
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Which methods can be used to evaluate the following integral?

How can I evaluate the following integral $$ \int_{0}^{\infty} x^{-1/2} \exp({-x/2})\ dx $$ I know the answer is $\sqrt{2\pi}$.

Published: Aug 12, 2026

quotient group Z/3Z equated to 0,1,2
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quotient group Z/3Z equated to 0,1,2

This a followup question on the first answer to this post: Why the term and the concept of quotient group? In the first answer, Lahtonen says that for the...

Published: Aug 12, 2026

Deriving the power series for cosine, using basic geometry
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Deriving the power series for cosine, using basic geometry

Looking for the derivation of cosine lead to https://www.quora.com/How-do-I-calculate-cos-sine-etc-without-a-calculator and the MacLauren series. $$\cos(x...

Published: Aug 12, 2026

Reflexive Transitive Closure
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Reflexive Transitive Closure

The problem I am working on is, "Show that a finite poset can be reconstructed from its covering relation. [Hint:Show that the poset is the reflexive tran...

Published: Aug 12, 2026

Prove that there are an infinite number of discontinuities on this function.
general

Prove that there are an infinite number of discontinuities on this function.

Show the function $f:[0,1]\rightarrow\mathbb{R}$ given by $$ f(x)= \begin{cases} 1,&x=\frac{1}{n}\text{ for any positive integer $n$}\\ 0,&\text{o...

Published: Aug 12, 2026

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