Recent content by michaelxavier

Homework Statement An urn contains $p$ black balls, $q$ white balls, and $r$ red balls; and $n$ balls are chosen without replacement. a. Find the joint distribution of the numbers of black, red, and white balls in the sample. b. Find the joint distribution of the numbers of black and white...

Homework Statement Find a sequence of differentiable functions $f_n\colon [a,b]\rightarrow\mathbb(R)$ s.t.: --there exists $M>0$ with $|f_n'(x)|\leq M$ for all $n\in\mathbb{N}$ and $x\in[a,b]$; --for all $n\in\mathbb{N}$, $|f_n(a)|\leq M$; --$(g_n)$ is a convergent subsequence with...

Are Li2SO4, Na2SO4, K2SO4, Ag2SO4, (NH4)2SO4, MgSO4, BaSO4, COSO4, CuSO4, ZnSO4, SrSO4, Al2(SO4)3, and Fe2(SO4)3 acidic or basic? On the one hand, Wikipedia says that (NH4)2SO4 and Al2(SO4)3 are acidic, and says nothing about the others. On the other hand logic seems to dictate that in a...

right, that's what i thought. you could in fact do that for every point. but then quasar said that doesn't work... now I'm confused.

okay. then what about points where such a ball consists of only a point?

That's good too. Also, how about, each x is a compact set (since for any open cover {Ga}, x is in some Ga1, so there is a finite subcover => x is compact), hence f is continuous at each x, hence f is continuous. does that work too? thank you!

right. but how do i prove that every point of X is part of a compact set? can i construct one? like, a closed ball around every point x would be compact, then i just have to choose the right radius. choose r s.t. B(x, r) is a subset of X, where B(x,r) is the closed ball of radius r centered...

Given epsilon positive, there exists positive delta s.t. d( f(x),f(y) ) < epsilon whenever d( x,y) < delta

Homework Statement Suppose that fk : X to Y are continuous and converge to f uniformly on every compact subset of the metric space X. Show that f is continuous. (fk is f sub k) Homework Equations Theorem from p. 150 of Rudin, 3rd ed: If {fn} is a sequence of continuous functions on E...

you would use taylor's for the whole thing, or just for f'(d) - f'(e) = f"(c)? thanks for replying, by the way.

Homework Statement Assume that f is twice differentiable on the entire real line. Show that f(-1) + f(1) - 2f(0) = f"(c) for some c in [-1,1] Homework Equations I'm thinking the mean value theorem will be helpful here -- the MVT states that, given a function f differentiable on [a,b]...

Oh, of course. Thanks so much!

Are you sure you aren't confusing domain and range? It's true that the wave is now compressed horizontally, but the sine will still stretch from negative infinity to infinity. On the interval (-pi,pi), the graph will repeat itself, but there is a graph there, so you can definitely make a table...

In Rudin's Principles of Mathematical Analysis, 3rd ed., I encountered the following on p. 10, and I'm not really sure where it comes from. I'll write it just as it is shown in the book. The identity b^n-a^n=(b-a)(b^(n-1)*a^0 + b^(n-2)*a^1 + ... + b^1*a^(n-2) + b^0*a^(n-1)) yields the...