first let me add a disclaimer, my question is not a duplicate of Find the number of 3-letter words that can be made with letters in alphabetical order. I ...

A common way to characterize the dirac delta function $\delta$ is by the following two properties: $$1)\ \delta(x) = 0\ \ \text{for}\ \ x \neq 0$$ $$2)\ \...

I know $\tan^2(x) \neq \tan(x^2)$ but I can't find an intuitive way to understand $\tan^2(x)$. When I do it in my mind I think: $\tan^2(x) = \left(\f...

Does the quadratic formula always work for a quadratic? If it does, why are the factors sometimes imaginary numbers?

I can see why distributive is called distributive (distribute whatever you are multiplying to everything within the brackets). Associative because when th...

This is blowing my mind away ... this should be easy stuff! Starting with the recursive formula $y_n=2n*y_{n-1}$ where $y_1=5.$ I'm trying to come up...

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...

Arc length $l$ can be calculated either by degrees or radians: $l = 2\pi r \times \dfrac{\theta}{360} \text{ (in degrees)}$ $l = r\theta \text{ (in radian...

Find the value(s) of $k$ for which the equation, $(x+2)(x+k)=-1$, has equal roots. (I cannot get the two values as stated in the answer $k=0$ and $k=4$. M...

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...