Recent content by KiwiKid

Wow, thanks. That's probably it. :smile: *starts writing it all down once more*

f(x) = arctan(x); The first derivative: f'(x) = 1/(x^2 + 1); Second derivative: f''(x) = -2x/((x^2+1)^2). ...And so on. Except that it's around the third derivative that it starts to get more complicated, and it becomes virtually impossible to keep differentiating without making mistakes. At...

Homework Statement Show that the fifth derivative of arctan(x) equals (120x^4 - 240x^2 + 24)/((x^2 + 1)^5). Then, calculate the fifth order Taylor series of arctan(x) around x = 0. Homework Equations Differentiation rules; knowing how a Taylor series works. The Attempt at a Solution I...

First of all, I wasn't quite sure in which (sub)forum to post this, so if it doesn't quite fit, feel free to move it. I'm having a very hard time solving this one (or even seeing if it's logically consistent), and any help would be very much appreciated. Homework Statement Give a formal proof...

I'd try to get everyone in the country free solar panels. I'm in the Netherlands, so I might actually get pretty far.

Ah, found it. I've been messing around with trigonometric identities for half an hour now. Turns out I just had to factor the whole equation. Thanks. =D

Homework Statement Solve 2cos(x)^2 + 3cos(x) + 1 = 0 for 0 <= x <= 2pi Homework Equations Trigonometric equations, yadda yadda yadda. The Attempt at a Solution 2cos(x)^2 + 3cos(x) + 1 = 0 cos(x)(2cos(x) + 3) = -1 cos(x) = -1/(2cos(x) + 3) I then figured out that you get a solution when...

Not sure if you're speaking solely about elections in the USA, but if not, I have a comment. During the election a month ago here (in the Netherlands), debates really *did* matter. The socialist party held about 40 seats in parliament in the polls, with the labour party having only 15 or so, but...

Nice save. :wink:

Challenge (verb) does not equal all of the definitions of challenge (noun).

And here I was thinking this thread was about natural math skills. Silly me.

Precisely.

I think daveb means that if someone tells you 'X is true', you can challenge it by saying 'is that so?' without necessarily having to have an opposing belief.

Were both tests administrated by a qualified psychologist? If so, these results were significant. If not, well, I'm not surprised - there are a lot of bad or incomplete 'IQ' tests. (And, of course, IQ tests don't measure everything, but they're reasonably at measuring mental 'processing power'.)

No, I don't see a problem with challenging those beliefs. Why? Because if they are correct (which I of course believe they are), then that's we'll conclude. Note that 'challenging beliefs' does not mean you can just ignore what is generally taken for granted - there are often good reasons for...