Recent content by fraggle

Thanks a lot, that made sense.

Can you please explain?

Homework Statement A coin is tossed 3 times. at least 1 head is obtained. Determine the probability that exactly 1 head is obtained Homework Equations The Attempt at a Solution brute force indicates that there 7 possible combinations: HHH, HHT, HTH, HTT, THH, THT, TTH...

A coin is tossed 3 times. at least 1 head is obtained. Determine each probability...? 1) exactly 1 head is obtained 2) exactly 2 heads are obtained 3) exactly 3 heads are obtained. ------------------------------------------------------------ for 1) brute force indicates that there 7...

Homework Statement Let f be a polynomial of degree n >= 1 with all roots of multiplicity 1 and real on R. Prove that f has at most one more real root than f' f' has no more nonreal roots than f Homework Equations We are given the Gauss Lucas theorem: Every root of f' is contained in...

Figured it out. Use http://www.texify.com/img/%5CLARGE%5C%21%5Cfrac%7B%7Bd%5E2%7Du%28x%29%7D%7Bd%7Bs%5E2%7D%7D%3D%5Cfrac%7Bd%7D%7Bds%7D%20%28%5Cfrac%7Bdu%7D%7Bdx%7D%20%5Cfrac%7Bdx%7D%7Bds%7D%29.gif Oops, I guess I don't know how to paste in the text. write out: d^2(u(x))/ds^2 then if...

Homework Statement Solve this differential equation http://www.texify.com/img/%5CLARGE%5C%21%5Cfrac%7B2%7D%7Bx%5E2%7D%28%5Cfrac%7Bdx%7D%7Bds%7D%29%5E2-%5Cfrac%7B1%7D%7Bx%7D%20%5Cfrac%7B%7Bd%5E2%7Dx%7D%7Bd%7Bs%5E2%7D%7D%3D1.gif (thanks Mark) where x is unknown, s represents the...

Homework Statement Is the Fundamental group of the circle (S^1) abelian? Not a homework question, just something I want to use. Homework Equations The Attempt at a Solution Intuitively it appears to be and it is isomorphic to the additive group of integers which is abelian. I...

thanks, that makes sense

Homework Statement Suppose A is an unbounded subspace of a metric space (X,d) (where d is the metric on X). Fix a point b in A let B(b,k)={a in X s.t d(b,a)<k where k>0 is a natural number}. Let A^B(b,k) denote the intersection of the subspace A with the set B(b,k). Then the...

Homework Statement Suppose f:X-->Y suppose for each open set U in Y s.t U contains some element f(x), we have f^(-1)(U) is open in X. Does this imply f is continuous Homework Equations U is not quite an arbitrary open set of Y since there could be an open set of Y that does not...

Prove Sin(x):R--->R is continuous Homework Statement Prove that Sin(x) from R to R is continuous using the epsilon delta definition of continuity and the following lemma: denote the absolute value of x by abs(x) Lemma: abs(x)>=sin(x) Homework Equations Could somebody please just...

But in the intervals [a,r_n] and [s_n,b] as n approaches infinity r_n and s_n approach x_0. Then we could take f(x_0) as supf(x) in those intervals, that is if n goes to infinity. So wouldn't the sum be equal to 2? If that is not the case could you please explain? thanks

Correct

The f is the f(x) defined in the statement. Sorry if that was not clear. I used the greek letter alpha "α" in the statement of the problem. I see that the font is kind of ambiguous. Both f and alpha "α" are functions defined on [a,b].