Recent content by Strants

I believe I have a solution to problem 2. Consider the complex polynomial p(z) = a_n z^n + a_{n-1} z^{n-1} + \cdots + a_1 z + a_0. Then, the roots r_i of p(z) are precisely the points of \mathbb{C} such that \oint_{C_\epsilon(r_i)} \frac{p'(z)}{p(z)} dz \not= 0 \tag{1} for all \epsilon...

One skill that I know I've used quite frequently in my intro. to analysis course was constructing inequalities. In my experience, inequalities aren't really taught (well, anyways) before analysis, so it might be worth practicing them now.

Well, for an odd function, f(-x) = -f(x). So, if f and g are odd functions, and h(x) = f(x)g(x), is h an odd function?

Just to make sure everyone's on the same page: adjacent, do you know trigonometric functions (Sine, Cosine, Tangent)?

This seems backwards: we generally say "as x approaches c, f(x) approaches L." I think of a limit as stating that, for x values "close" to c, we can make f(x) as close to L as we want. 0 < |x - c| < \delta denotes a deleted neighborhood of c - basically an interval centered on c, but with...

I disagree here; order doesn't matter for any group of men, and as such the choose function should show up here. As far as the OP's elimination method goes, again, order does not matter. How many 'illegal' committees are there? (Hint: think about how many more men there are to choose from...

It would be possible if you also knew V & ~C, though. Since A & B only has ones where both A and B have ones, and ~B has ones only where B has zeros, V & ~C has the 'missing ones' from the other calculation.

Are you sure about that partial fraction simplification? I get \frac{1}{rx} - \frac{x}{r(r+x^2)}

Well, what does the condition x≥3 mean for the equation f(x)=(x-3)^2 -1 ?

I would assume the phrase "approaches infinity in finite time" means the graph has an asymptote.

Actually, I believe the identity is \sin x = \frac{-i(e^{ix} - e^{-ix})}{2}.

I get the feeling micromass meant to say a, -b, and c. I also think he was getting at this: what would the sides of the triangle be?

It looks like you tried to distribute the natural log over addition, which doesn't work. The left hand side is fine, but the right hand side should be \ln (y^2 \cos(x) + y) Or I suppose you could divide out the y from the original expression, but that won't really help, seeing as you'd just...

Do you mean \frac{\sqrt{-5t+400}}{5} or \sqrt{\frac{-5t+400}{5}} The first equation is correct, and the same as you have, though they simplified it a little, which might not be a bad idea. Try to make the denominator of the fraction a square, and then you can move it outside the root.

You need to square root the whole left side, not just the numerator. So sqrt( (80-t)/5) = h. From what you have, it looks like you take the square root of 80-t, then divide by 5, which is not the same.