While I was reading about conic sections, I came across the following statement: A parabola is an ellipse, but with one focal point at infinity. But it is...

Fundamental theorem of calculus states that the derivative of the integral is the original function, meaning that $$ f(x)=\frac{d}{dx}\int_{a}^{x}f(y)dy.\...

If matrix $A$ is given with dimensions $2 \times2 $ then, A is invertible if, and only, if $ad - bc \neq 0$: $$\begin{bmatrix}a & b\ \\c & d \ \en...

How does one calculate the indefinite integral? $$\int\frac1{\sigma\sqrt{2\pi}}\exp\left(-\frac{x^2}{2\sigma^2}\right)dx$$ Where $\sigma$ is some constant...

I got $\cos 2B$; $\cos 2B=2 \cos^2 B - 1 =9/8 -1 =1/8$ but when I tried cos1/2B, I got: COS1/2B=cos^2*1/4B-1, then I solved it, and didn't get the an...

I thought of this a while ago, but can't make up a proof or a counterexample. Does anyone know more about this? $$\sqrt{a+b} \le \sqrt a + \sqrt b , ...

This is assuming that the function is in a fractional form where the the degree of the numerator is higher than the degree of the denominator.

Suppose I knew nothing about the function $e^x$. If I wanted to find a power series that was its own derivative, I would logically start with the constant...

I'm reading the proofwiki page about complex number: https://proofwiki.org/wiki/Definition:Complex_Number According to proofwiki there is an informal...

emm, I got this problem on a text book and it looked nice to done with, but I'm really unsure about my answer because it goes into a non-elementary e...