I have the following stepwise function: $$f(x) = \begin{cases} \frac{1}{3} & -1\le x \lt 0 \\ \frac{2}{3} & 0 \le x \le 1 \\ 0 & \text{otherwi...

I needed to evaluate the surjectivity of cuberoot(x) and used Wolfram-Alpha for that. To my surprise, cuberoot(x) is different than x^1/3, as can be seen ...

Consider a function $g: \mathbb{R^3} \to \mathbb{R}$ defined by $g(x,y,z) = z^2 -x^3 + 2z + 3y^3$ Find the gradient of $g$ at the point $(2,1,-1)$. Is the...

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 ...

I was using the TI-84 Plus calculator to check for Y-Axis symmetry in the graph of "cos(2X+1)" and as I had to do it fast (I was in the middle of a test),...

I'm not sure how to ask but I hope you will understand. Let's say we have such root: $$m\sqrt[2] n$$ or $$2\sqrt[2]3$$ So could you please tell ...

In linear algebra, the kernel of a matrix is its null space. In machine learning and statistics, there are a bunch of matrices are called "kernel". For ex...

I've recently read about the Fundamental Theorem of Arithmetic and I think that I have just about understood the proof. What I found quite interestin...

This the problem from the test and I'm stuck at one part. Matt will arrange four identical, dotless dominoes (shaded 1 by 2 rectangles) on the 5 by 4...

I'll get to the point immediately. The definition of divergence in a point (from my textbook): $$ div \bar{E} = \lim_{V \to 0} \frac{1}{V}\oint_S \ba...