How to evaluate $$\lim_{(x,y) \to (0,0)} \frac{ax^2+by^2}{cy^2+dx^2} $$ using $y=mx$? Here what I've done: \begin{align*} \lim_{(x,y)\to(0,0)}\frac{a...

We have the system $y''=-7y'-12y-u'-2u$ If we choose $x_1=y,x_2=y'$ we can write the system as $x'=Ax + Bu \\ y= Cx$ Finding...

Is the following statement true? Suppose we are given $f(x)$ defined and differentiable $\forall x \in \mathbb{R}$, $x\neq 0$. If $xf'(x)>0$, then...

Is there an easy way to draw lines on a graph to be at certain angles using only rise/run? For example, to make a 45 degree angle with the x axis, the ris...

I often see mathematical notation on Wikipedia articles (e.g. Finding the matrix of a transformation). Where is a good resource for learning what the diff...

The wife and I are sitting here on a Saturday night doing some algebra homework. We're factoring polynomials and had the same thought at the same tim...

How to prove that the composition of 2 rotations about an axis $l_1$ and $l_2$ is the rotation? I know that we can represent rotation about the axis $l$ a...

I am attempting to work on some proofs for my math assignment, but I'll be honest in that I am really struggling to understand them. I read through t...

If the determinant $\det(A)$ of the matrix $A$ of a non-homogeneous system of equations is $0$, then how do we know if it has no solutions or infinitely m...

I have the following data: $$\begin{array}{c|c|c}2010 & 2011 & 2012 \\\hline 50 & 20 & 30 \\\end{array}$$ How would the percent change be ...