This question refers to the Rees ring, and can be posed from first principles as follows. Let $A$ be a Noetherian ring, $t$ an indeterminate over $A$ and ...

Assume that $f(x),g(x)$ are positive and are in $L^1$. Moreover, they are differentiable and their derivative is integrable. Let $h(x)=f(x)*g(x)$, the con...

Find a vector function that represents the curve of intersection of following two surfaces: the cone $z=\sqrt{x^2+y^2}$ and the plane $z=1+y$. This is a q...

According to the Wikipedia article, [Euler] introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, s...

A rational preferences (that is, complete and transitive) are continuous. Then how can I show that there exist a continuous function u(x) that represents ...

Let $A$ be an m*n matrix with entries from a field $F$. $L_A: F^n \rightarrow F^m$ defined by $L_A=Ax$. I'm a bit confused about this definition. $L_...

So I understand that the volume formula of a cone is: $\frac{1}{3}\pi r^2h$, and when I read about how to derive this formula, it makes sense to me. Funny...

I am reading a book and it says to solve limits to infinity with a fraction such as: $$\frac{5X^2 + 8X - 3}{3X^2 + 2}$$ We divide the numerator and denomi...

At what point of the parabola $y=x^2-3x-5$ is the tangent line parallel to $3x-y=2$? Find its equation. I don't know what the slope of the tangent li...

Why does the Mandelbrot set appear when I use Newton's method to find the inverse of $\tan(z)$ Specifically for the equation $y = \tan(z)$ I use Newt...