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Best CAPTCHA ever [Jul. 19th, 2007|10:52 am]
 [ Tags | funny, tech ]

A CAPTCHA gives you a little test to see if you're human, not a computer auto-generating accounts.

You know, this sort of crap:

But these guys have a way better one:

From:
2007-07-19 07:20 pm (UTC)

### possibly embarrassing myself here

I forget calculus syntax. Is that asking you to just evaluate at x=2pi?
In that case, the sin is +1 and the cos is -1 at that point, so it's just 7 - 4 = 3.
From:
2007-07-19 07:54 pm (UTC)

### Re: possibly embarrassing myself here

You mean I was only off by 4?! Not bad!
From:
2007-07-19 08:22 pm (UTC)

### Re: possibly embarrassing myself here

You have to take the derivative first, then evaluate it at the point x=2pi. Anyway, sin(N*2pi)=0, cos(N*2pi+pi/2)=0.
From:
2007-07-19 09:22 pm (UTC)

### Re: possibly embarrassing myself here

I meant "evaluate the derivative", and "the sin is +1" I meant "the derivative at that point is +1". Nikolas did it more thoroughly below.
From:
2007-07-19 09:45 pm (UTC)

### Re: possibly embarrassing myself here

He messed up too. :) Must be a lot of programmers hanging around here, and not enough engineers.
From:
2007-07-19 10:18 pm (UTC)

### Re: possibly embarrassing myself here

I think you both forgot to apply the chain rule. The derivative of 7Sin[6x] is 42 Cos[6x], etc.
(Deleted comment)
From:
2007-07-19 09:23 pm (UTC)

### Re: Spelling it out ...

Alternatively, what I did was visualize what the derivatives at those well-known points are: the sin is maximally sloping upwards (+1) and the cos maximally downwards (-1), which got me to your second-to-last step without computing any derivatives directly. :)
From:
2007-07-19 09:44 pm (UTC)

### Re: Spelling it out ...

You missed a factor on the derivative. D[ sin(ax) ] = a*cos(ax) . Remember D[ sin(u) ] = cos(u)du . See my solution above.
From:
2007-07-19 10:15 pm (UTC)

### you forgot the chain rule

has the correct answer above, 14.