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by Eebster the Great
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 ...
by Eebster the Great
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.
by Eebster the Great
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...
by Eebster the Great
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 ...
by Eebster the Great
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 ...
by Eebster the Great
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...
by Eebster the Great
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...
by Eebster the Great
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...
by Eebster the Great
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...
by Eebster the Great
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...

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