Recent content by llursweetiell

oh that makes sense. thank you so much! =)

okay how about this: A=not open, not closed and therefore, not compact; accum. pt: [0,2] B=closed, and compact; accum pt: empty set C=open, and not compact; accum pt: empty set D=not open, not closed and therefore, not compact; accum pt: empty set E=open, and not compact; accum pt: empty...

here's what I've come up with for the accumulation points: A=[0,2] B=Z C=empty set D=sqrt(2) E=empty set. any help anyone?

Here is what I've come up with: let f(x)=x/(x+1) let P be the partition {x0, x1, ...xn} where xi=i/n and ti=xi and the mesh is 1/n=xi-xi-1 (i and i-1 are subscripts) then S(P,f)=SUM: f(ti)(xi-xi-1) = SUM: 1/(n+1) * 1/n, from i=1 to n which is the sequence an. since S(p,f) converges to the...

I'm thinking that the partition would be P= 0=x0<x1<x2<...,xn=1 with 1/n partitions. Not sure about how this would relate to the sum that I have in the problem?

So i wrote, We know that f is continuous at a. to prove that g is continuous at a: let epsilon be greater than 0 and let delta > 0 such that d=epsilon/(f(x)^{n-1} + f(x)^{n-2}f(a) + ... + f(a)^{n-2}f(x) + f(a)^{n-1}) then, for |x-a| < delta, then |f(x)^n-f(a)^n|=f(x)^n - f(a)^n =...

Homework Statement Can someone check this for me? Problem: determine which, if any of the sets if open? closed? compact? R=reals; Q=rationals and Z=integers. A= [0,1) U (1,2) is NEITHER B=Z is CLOSED C=(.5,1) U (.25,.5) U (.125, 25) U... is OPEN D={r*sqrt(2) such that r is an element of...

the problem states: suppose f:D--> R is continuous at a. Let n >1 be a positive integer. Using the epsilon and delta definition of continuity, prove g(x)=[f(x)]^n is continuous at a. Does that help? Also, the composition way did not work. which is why I'm unsure of how to go about...

Homework Statement consider the sequence {an} where an= 1/(n+1) + ...+ 1/2n. find its limit. Homework Equations the hint given is using riemann sum. The Attempt at a Solution we know that since it is increasing and bounded above by one, the sequence converges. I'm not sure where...

Homework Statement Suppose f: D-->R is continuous at a. Let n >1 be a positive integer. using the epsilon-delta definition of continuity, prove g(x)=[f(x)]^n is continuous as a Homework Equations i know how to do it as a sequence proof; but i don't know how to use the epislon/delta...