I have 6 digits (e.g: 1,2,3,4,5,6), then I use these digits to form a sequence of six digit pairs. Each digit in the given set can be used twice, and only...

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Finally got to double angles. Anyways I need to show that these are identities. $$\sin(4x) = 4 \sin(x) \cos(x) \cos(2x)$$ The book does some magic and get...

A series-reduced tree is defined as a tree with no vertices of degree 2. The word "reduced" suggests that there is a process for reducing trees that have ...

Someone asked me: "I am a teacher with 30 students. I want to arrange my students into groups that they meet with throughout the year. I'd like to ha...

Suppose $G : \mathbb R^n \to \mathbb R$ is a differentiable function and the level set $L = \{x \in \mathbb R^n: G(x)=0 \}$ is an $n-1$ dimentional surfac...

I know that integrals are used to compute the area under a curve. Let's say I have $y = x^2$. It creates smaller rectangles and then add up the sum (...

A naive question about axiomatic set theory I'm trying to teach myself some basic set theory by reading Set Theory for the Working Mathematician by K...

By division law, $$\displaystyle \lim_{x \to \infty} \dfrac{\sqrt[3]{x^2+8}}{x+2}$$ is equivalent to $$\dfrac {\displaystyle \lim_{x \to \infty} {\sqrt[3]...

I was looking to the volume created if I revolve the area of the pentagon having vertices (1,0), (2,2), (0,4), (-2, 2), (-1,0) about the x-axis. My work: ...