Recent content by mrchris

Maybe I have nod idea what I am talking about, but I am pretty sure that to prove this one theorem, I only need to demonstrate that one such partition exists. my professor made that very clear. you can find a partition for any integrable function's domain that will make the condition limit as...

i guess i also could have kept writing 3 beside the limits but again, this wasn't mentioned and even though I did disregard it, if the limit of something is zero as n --> inf, then 3 times that limit won't change anything.

Homework Statement I am a student in advanced calculus and I am having an issue with a grade I just received. the question was as follows: If a function f:[0, 3]→ℝ is continuous use the Archimedes Riemann theorem to show that f is also integrable. I want to take my answer to my...

so H ''(x) should then be of 2[ f '(x) - f '(−x)].

so i am under the impression that d/dx of ∫f(t) dt = f(x), so taking each term, H'(x)= dH/dx of ∫0 to x [f(t)]= f(x) ∫0 to x [f(-t)]= f(-x) ∫0 to -x [f(t)]= f(-x)*-1 ∫0 to -x [f(-t)]= f(x)*-1 so H'(x)= [f(x)+f(-x)]-(-1)[f(-x)+f(x)]=[f(x)+f(-x)]+[f(-x)+f(x)]=2[f(x)+f(-x)] I am not sure...

Homework Statement Suppose that the function f : R → R is differentiable. Define the function H: R → R by H(x) = ∫−x to x of [ f (t) + f (−t)]dt for all x in R. Find H'' (x). Homework Equations The Attempt at a Solution i divided it up into ∫ 0 to x of [ f (t) + f (−t)]dt and -∫...

Case 1: S is not bounded above. So this is a direct contradiction to the definition given for a maximum in the book, "a member c of S is called the max of S provided that it is an upper bound for S". Since S is assumed to be unbounded, no number c exists s.t. c is an upper bound for S. Case...

Homework Statement Sorry that should read and sup S\inS Homework Equations just the definitions of sup, inf, boundedness, and max The Attempt at a Solution I have tried a few different things, but this question is posted for advice, not just an answer. I am trying to think of a...

Thanks for the advice, both of your answers seem to make sense, but I am in an analysis class and I can only use what I've learned in the class so far in my proofs. We definitely haven't worked with prime factorization officially yet, so even though that argument may be more straight forward, I...

Homework Statement if n is a natural number and n2 is odd, then n is odd Homework Equations odd numbers: 2k+1, where k is an integer even numbers: 2K, where k is an integer The Attempt at a Solution ok so take the opposite to be true, or n2 is odd and n is even. Then we would have...

Homework Statement The set of squares of rational numbers is inductive Homework Equations definition of an inductive set The Attempt at a Solution sorry i know this is probably very easy to most but I am just learning analysis. Okay, so we can see that 1 is in the set because it is...

If i try to use the proof I did earlier with the 3 cases, I can not have g(h) not defined at any points because we are told f is differentiable.

why couldn't you arbitrarily pick any two endpoints such that a<b in ℝ and then proceed with the definition of the MVT?

i am not sure what is wrong with the proof using the MVT and c in (c-h, c+h). I also am not sure how to use the definition of the limit here. Is it not enough to say that since we are taking h>0, as h approaches 0, those values of h will all be positive? and also, if g(0) is undefined, doesn't...

I also realized that my previous post did not prove that f '(x)< 0 if h=0. When using that definition of the derivative, do I need to address the case of h=0?