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
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
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
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
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
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
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
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. $$\cos(x...
Published: Aug 12, 2026
The problem I am working on is, "Show that a finite poset can be reconstructed from its covering relation. [Hint:Show that the poset is the reflexive tran...
Published: Aug 12, 2026
Show the function $f:[0,1]\rightarrow\mathbb{R}$ given by $$ f(x)= \begin{cases} 1,&x=\frac{1}{n}\text{ for any positive integer $n$}\\ 0,&\text{o...
Published: Aug 12, 2026