## Search found 2610 matches

- Sat Oct 31, 2009 7:15 am UTC
- Forum: Mathematics
- Topic: Discontinuous derivative of an explicitly defined function
- Replies:
**18** - Views:
**4248**

### Re: Discontinuous derivative of an explicitly defined function

Yeah, and x^2sin(1/x) doesn't work either, not being differentiable at zero. Well, it's not even defined at 0. However, if you meant the function f \left( x \right) = \left\{ \begin{array}{ll} x^2 \sin \left( \frac{1}{x} \right) & \mbox{if } x \neq 0 \\ 0 & \mbox{if ...

- Sat Oct 31, 2009 7:01 am UTC
- Forum: The Help Desk
- Topic: Cannot login on Firefox
- Replies:
**4** - Views:
**537**

### Re: Cannot login on Firefox

poxic wrote:Try deleting all your forum cookies for forums.xkcd.com . That's the standard advice, and it usually works.

Thanks! I didn't realize recent logins were saved in cookies; I thought you just stayed logged in on that IP until you were inactive for a while.

- Fri Oct 30, 2009 7:44 am UTC
- Forum: Science
- Topic: "Homeopathy with Dr. Werner"
- Replies:
**46** - Views:
**5896**

### Re: "Homeopathy with Dr. Werner"

The thing I hate most about these kinds of people is how they propagate pseudo-science, stuff that sounds right to the uneducated but is horribly wrong. If the government is really interested in raising the education rates they should ban pseudo-sciences from children and enhance shows like mythbus...

- Fri Oct 30, 2009 6:06 am UTC
- Forum: Mathematics
- Topic: So, does this work as a prrof that e^pi*i=-1?
- Replies:
**39** - Views:
**3281**

### Re: So, does this work as a prrof that e^pi*i=-1?

At least, I think it comes in handy, because it's surprising how many math majors forget those formulas when they need them. There is also a similar strategy to quickly get the antiderivatives of sin^n (x), because those are a pain to remember. Seriously, how often will you need to know the triple ...

- Fri Oct 30, 2009 5:32 am UTC
- Forum: Mathematics
- Topic: Discontinuous derivative of an explicitly defined function
- Replies:
**18** - Views:
**4248**

### Re: Discontinuous derivative of an explicitly defined function

How about this function: f \left( x \right) = \left\{ \begin{array}{ll} x^2 \sin \left( \frac{1}{x} \right) & \mbox{if } x \neq 0 \\ 0 & \mbox{if } x = 0 \end{array} \right. It is differentiable everywhere, even at 0, as can be checked. But it's derivative is not continuous ...

- Fri Oct 30, 2009 5:17 am UTC
- Forum: Mathematics
- Topic: Taylor Series
- Replies:
**10** - Views:
**872**

### Re: Taylor Series

The solution needs to be sine and cos by looking at its properties. We want a function that when you take its derivative twice, you get the function times -1. This is sine and cos. Now you might say "There could be more functions that satisfy this!". They are, but by the uniquness of diff...

- Thu Oct 29, 2009 6:10 am UTC
- Forum: Mathematics
- Topic: translate Math comic in xkcd style
- Replies:
**6** - Views:
**1824**

### Re: translate Math comic in xkcd style

Try this: First panel: "We cannot finish our operation, my Lord." Second panel: "There is an irrational number . . . in the denominator again." ( Any better suggestions here? It might be better not to try to stick to the original format, as it gets kind of awkward in English ) Th...

- Thu Oct 29, 2009 5:52 am UTC
- Forum: Mathematics
- Topic: Discontinuous derivative of an explicitly defined function
- Replies:
**18** - Views:
**4248**

### Discontinuous derivative of an explicitly defined function

I am having trouble thinking of explicitly defined, differentiable functions with discontinuous derivatives in one dimension. This has been a problem that has bothered me since BC Calc, when I was presented an example of an integrable, discontinuous function defined piecemeal by its derivative. This...

- Thu Oct 29, 2009 5:34 am UTC
- Forum: Mathematics
- Topic: Taylor Series
- Replies:
**10** - Views:
**872**

### Re: Taylor Series

My preferred proof for Euler's formula is simply solving a second-order differential equation, although to be rigorous it technically requires proving some differentiation formulae for complex numbers. d^2/dx^2 e^(i x) = d/dx i e^(i x) = i^2 e^(i x) = -e^(i x) So solve the diff eq: d^2y/dx^2 = -y Th...

- Thu Oct 29, 2009 5:23 am UTC
- Forum: The Help Desk
- Topic: Cannot login on Firefox
- Replies:
**4** - Views:
**537**

### Cannot login on Firefox

This problem is odd, but I cannot login to this forum on Firefox, which is by far my prefered browser. After clicking "submit" in the login form, I do go to the page saying I logged in, but when it redirects me to the forum (or anywhere else) it clearly indicates that I am NOT logged in, a...