# Tagged Questions

2k views

### Is x*tan(x) integrable in elementary functions?

Dear All, I'm teaching Calculus and my students asked me to calculate the integral of x*tan(x). I spent quite a lot of effort to do this, but I'm now even not sure if the integral could be presented ...
697 views

### Another Chicken or Egg: Sequence or Series

This is a side question which is more motivated by teaching than research. First, I am trying to convince myself that sequences appear before series (as numerical approximations to "interesting" ...
2k views

### Taylor's theorem and the symmetric group

Anytime I see an $n!$ in some formula, my instinct is to look for the symmetric group on $n$ letters coming in somewhere. I have never done this seriously with the $n!$ in Taylor's theorem. Question: ...
2k views

### Taking “Zooming in on a point of a graph” seriously.

In calculus classes it is sometimes said that the tangent line to a curve at a point is the line that we get by "zooming in" on that point with an infinitely powerful microscope. This explanation ...
2k views

### Leibnizian calculus textbook

Where can I find a calculus textbook that emphasizes differentials? Is there such a book that I could realistically require my calculus students to use? I want a textbook that supports me when I tell ...
737 views

### Can formally differentiating give a derivative of a discrete function?

When I teach calculus, I really try to stress the importance of knowing the domain of a function. One example that I sometimes like to use to show students the importance of inspecting the domain is ...
2k views

### What is the simplest, most elementary proof that a particular number is transcendental?

I teach, among many other things, a class of wonderful and inquisitive 7th graders. We've recently been studying and discussing various number systems (N, Z, Q, R, C, algebraic numbers, and even ...
4k views

### The role of the mean value theorem (MVT) in first-year calculus.

Should the mean value theorem be taught in first-year calculus? Most calculus textbooks present the MVT just before the section that says that if $f'>0$ on an interval then $f$ increases on that ...
11k views

### Why does undergraduate discrete math require calculus?

Often undergraduate discrete math classes in the US have a calculus prerequisite. Here is the description of the discrete math course from my undergrad: A general introduction to basic ...
3k views

### Making sure that you have comprehended a concept

Hi, I have a question that I've been thinking about for a long time. How can you assure yourself that you've fully comprehended a concept or the true meaning of a theorem in mathematics? I mean how ...
So first I gave my class the quiz problem: Compute $$\lim_{h\rightarrow 0} \frac{\frac{1}{3+h} - \frac{1}{3}}{h}.$$ Upon finding that they could not do that (no real surprize) I asked them to compute ...