## Top new questions this week:

### What did mathematicians study as an undergraduate/graduate before modern mathematics such as modern algebra and analysis?

I am curious as to what mathematicians such as Leibnitz and Gauss and the Bernoulli's studied when they were students in university. I find it fascinating how we are taught calculus and abstract ...

(soft-question) (math-history) (education) (big-list) (mathematicians)

### Can you cancel out a term if equal to zero?

quick question here: In my proofs class we had a problem that after a little work we end up with: $x(x-y)=(x+y)(x-y)$ where $x = y$. Now, I know this is pretty basic, but my teacher said that for ...

(algebra-precalculus)

### A function having limit at every point but continuous nowhere

Is there a function $\,f:\mathbb{R}\rightarrow\mathbb{R},\,$ that has a limit at every point but is continuous nowhere?

(calculus) (real-analysis) (analysis) (limits) (continuity)

### Explain $x^{x^{x^{{\cdots}}}} = \,\,3$

$$x^{x^{x^{\cdot^{\cdot^{\cdot}}}}} =\quad 2$$ This equation has the answer $\sqrt{2}$ by taking $\log$ to both side. This answer is correct because I'd proved it by computing the equation repeatedly ...

(algebra-precalculus) (limits) (tetration) (power-towers)

### Dividing by 2 numbers at once, what is the answer?

Let's say i have 4/1/5. or 4 divided by 1 divided by 5. Are there any rules that i am allowed to use to stop any mistakes?, for example this has 2 solutions, 4/5 , and 20. Edit: Thanks for your ...

(notation) (fractions)

### Time-optimal control to the origin for two first order ODES - But wait, the node is unstable? Hard-mode active!

I want to find the time optimal control to the origin of the system: $$\dot{x}_1 = 3x_1+ x_2$$ $$\dot{x}_2 = 4x_1 + 3x_2 + u$$ where $|u|\leq 1$ I ran straight into the problem full strength, hit it ...

(optimization) (calculus-of-variations) (optimal-control)

### Evaluation of $\int_0^{\pi/4} \sqrt{\tan x} \sqrt{1-\tan x}\,\,dx$

How to evaluate the following integral $$\int_0^{\pi/4} \sqrt{\tan x} \sqrt{1-\tan x}\,\,dx$$ It looks like beta function but Wolfram Alpha cannot evaluate it. So, I computed the numerical value of ...

(calculus) (real-analysis) (integration) (definite-integrals) (closed-form)

## Greatest hits from previous weeks:

### Visually stunning math concepts which are easy to explain

Since I'm not that good at (as I like to call it) 'die-hard-mathematics', I've always liked concepts like the golden ratio or the dragon curve, which are easy to understand and explain, but are ...

(soft-question) (education) (big-list)

### Demystify integration of $\int \frac{1}{x} \mathrm dx$

I've learned in my analysis class, that $$\int \frac{1}{x} \mathrm dx = \ln(x).$$ I can live with that, and it's what I use when solving equations like that. But how can I solve this, without ...

(integration) (indefinite-integrals)

### Ratio of product from one point and minimum distance

Given points $A_0,A_1,\ldots,A_n$ in the plane, let $m$ denote the minimum distance among any two points. What is the minimum value of $$\dfrac{|A_0A_1|\cdot|A_0A_2|\cdot\ldots\cdot|A_0A_n|}{m^n}?$$ ...

(inequality) (contest-math) (combinatorial-geometry)

### $\int\limits_{a}^{b} f(x) dx = b \cdot f(b) - a \cdot f(a) - \int\limits_{f(a)}^{f(b)} f^{-1}(x) dx$ proof

I just wanted to ask, if my proof is correct. I haven't seen the equation before, but I think it's quite useful. Let $f$ be an bijective differentiable function. Then the inverse function $f^{-1}$ ...

(real-analysis)
I'm reading Donal F. Connon, Some integrals involving the Stieltjes constants. It gives a definition of the generalized Stieltjes constants $\gamma_n(u)$ as coefficients in the Laurent series ...