# challenge

1. ### Challenge problem

I believe this is technically a calculus problem so lll post this in this area of the forum. The problem is as follows, though you will have to forgive me if I don't do a good job at posting the problem. sum of the series from d=2 to infinity with equation e^(sum of the series k=1 to...
2. ### challenge problems

If sin A=1/squareroot 3 with 0<A<pi/2, and cos B= -1/2squareroot3, with pi/2<B<pi, calculate a)cos(A+B) b) sin(A+B) c) cos2A d) cos A-B)
3. ### Challenge 2

Alright, I am not even really sure how to start this problem. The idea is to derive the equation for the given parabola: Focous- (2,2) Directrix= y=-x I know how to derive an equation if the parabola starts on the origin, but how do you go about doing it when it is off of the...
4. ### Challenge

Here is something I found challenging, thought I would share. I'm off to work, but I think I'll put a bit more time into it tonight when I get home because it is a little hard for me. I found it with my calculator but that is cheating. Here is the key, no calculator! Solve: acrtan(1) +...
5. ### Challenge Problem

Does anyone know how to do this? Find a function f such that f(1) = -1, f(4) = 7 and f '(x) > 3 for all x. Or prove such a function does not exist.
6. ### Challenge: from a previous Ohio Math League contest

A semicircle is inscribed in a unit square such that the two endpoints of the diameter lie in two sides and the semicircle is tangent to the other two sides. Find the area of the semicircle (preferably an exact value in terms of square roots and pi).
7. ### Challenge: standard equation for conic sections

Find the standard second degree equation in two variables for a conic section with eccentricity e, focus (xsub1,ysub1), and directrix y=k, in terms of e, xsub1, ysub1, and k. The equation should be of the form ax^2 + bxy + cy^2 + dx + ey +f. If you saw the answer in a post in...