Recent content by kirstin.17

Have no idea what Dirac Delta Distribution is... haven't learned that.

Homework Statement The integral of f on [a,b] exists and is positive. Prove there is a subinterval J of [a,b] and a constant c such that f(x) >= c > 0 for all x in J. Hint: Consider the lower integral of f on [a,b] Homework Equations The Attempt at a Solution I don't see how...

Aha... I would say there are no other solutions other than what I already mentioned. First note that the last expression you stated is equivalent to the original one we want to solve. Solutions will occur either where (a-1)\sin^{2}(x)=0 and (b-1)\cos^{2}(x) =0, or where...

I'm trying to solve this trig problem: sin^2000(x) + cos^2000(x) = 1 I'm not sure how to go about it... I tried starting with sin^2(x) + cos^2(x) = 1 and build up to 2000 but I didn't get very far. Obviously any multiple of pi will be an answer since either sin^2000 or cos^2000 will be...

I voted quite abstract. Some people can't appreciate beautiful proofs but some are just so clever and amazing... how would anyone have thought of that!?... It's beautiful.