Recent content by embemilyy

thanks for responding! If A, B, and C are infinite, I think the statement holds (just by results of cardinal arithmetic that I've seen in the textbook), but I'm still not able to find a bijection.

Homework Statement Prove that |AB\cupC|=|ABx AC| by demonstrating a bijection between the two sets. Homework Equations Two sets have equivalent cardinality if there is a bijection between them/ The Attempt at a Solution Essentially I can prove that there is a function from...

I think so! If \sum\sqrt{an}/n diverges, then the limit as n approaches infinity of (\sqrt{a(n+1)}/(n+1))/\sqrt{an}/n is greater than or equal to 1, which implies that the limit as n approaches infinity of \sqrt{a(n+1)}/\sqrt{an} is greater than or equal to 1, which implies that the limit as...

Homework Statement If \sum(an) converges, and an>0, prove that \sum\sqrt{an}/n converges Homework Equations The Attempt at a Solution I'm trying to use the comparison test, since an>0. So I have to prove that an>\sqrt{an}/n. But I keep getting stuck here because an approaches zero, so an is...

Any ideas?

I was thinking of it as the region outside of the cone, above the xy-plane

Thanks for responding! Sorry about that, I just posted the density. density= (x2+y2)1/2. It is bounded between the cone, the cylinder, and the plane z=0. So I'm thinking the z bounds must be z=0 to z=r. I'm having trouble coming up with the bounds for r though, because of the shift in the...

Find the mass of the solid bounded by the cylinder (x-1)2 + y2=1 and the cone z=(x2+y2) 1/2 if the density is (x2+y2) 1/2 I know that I have to substitute for cylindrical co-ordinates x=rcos(theta), y=rsin(theta), and z=z, and then use the change of variables formula to get the mass by...