# Search results

1. ### Inverse composite proof (wording of the proof)

This is the part that confuses me. Should I be saying something to the effect: For any a\inA there exists a unique b\inB and a unique c\inC such that f(a)=b and g(b)=c. It follows that g(f(a))=c. Thus (g o f)^(-1)(c)=a
2. ### Inverse composite proof (wording of the proof)

"Since c is arbitrary, it suffices to prove that (g∘f)−1(c)=a as well. How can you do that?" I don't quiet understand your question, or the statement before it.
3. ### Inverse composite proof (wording of the proof)

Homework Statement Let f:A->B and g:B->C be invertible mappings. Show (g o f)^-1 = f^-1 o g^-1. Homework Equations A mapping is invertible iff it is bijective The Attempt at a Solution I understand why these are equivalent statements; however, I can't figure out the wording of the...
4. ### Proving the pigeonhole directly. I'm stuck.

Yeah I guess that would work since things are equivalent if they are a bijection. Thanks man
5. ### Proving the pigeonhole directly. I'm stuck.

Homework Statement Prove the pigeonhole principle directly. so basically |Nk-{x}|=|Nk-1| if k>1 is an integer and x belongs to the set of naturals. Homework Equations The Attempt at a Solution I have no idea even where to begin.
6. ### A quick question on Summations.

this is what i get for only half paying attention to what i type. damn finals. 2^k, Sorry bout that
7. ### A quick question on Summations.

sorry i meant to say 2^n for the eq.
8. ### A quick question on Summations.

I can never remember how to expand a summation in to form: \sumnk=1(22). Thats just a recent example. I can't remember the expansion form any sort of summation really except when it has a defined upper bound.
9. ### What is the derivative of (tan(x))^(1/x) and sqrt((x-1)(x^2 (x-4)))?

It would be the chain rule but in tandum with the product rule which I forgot to do anyway, and thank you for catching that.
10. ### What is the derivative of (tan(x))^(1/x) and sqrt((x-1)(x^2 (x-4)))?

Sorry this took so long. Originally I was looking at how you did it not the question and what the answer should be. You forgot a negative from d/dx(1/x) but I'm pretty sure you can't do it that way. As far as I know you can approach this straight on or using a ln trick. I'll show both...
11. ### What is the derivative of (tan(x))^(1/x) and sqrt((x-1)(x^2 (x-4)))?

Well the only mistake I see in your first work is that you forgot a negative. and for the second problem break it down to a more simple problem. It may become more work to resimplify it later but you aren't wrong to do so. You can take it and make it into this d/dx((x-1)(1/2)/(x2(x-4))(1/2))...
12. ### Continuous function, integral

You were right in the fact that a direct proof would be much to hard for this problem, but a contradiction is hard to come up with. See if you can prove it by contrapositive Suppose f(x) doesn't equal zero, however according to your givens it has to be greater than or equal to zero , then it...
13. ### Kinda Urgent. Proof Wriiting. Squences

Ok this isn't so urgent any more but my teacher loves to just stare blankly at me like I'm stupid when I ask questions so I'd like to continue here with anyone who will help. I got to |(Y[n]*L-M*L+M*L-X[n]*M)/X[n]*L|<epsilon in which i then factored |(L*(Y[n]-M)-M*(X[n]-L))/X[n]*L|<epsilon. I...
14. ### Kinda Urgent. Proof Wriiting. Squences

Could you clarify this at all. What i sounds like you are saying to me is that I should be supposing the consequent but that is uber taboo. I mean I could suppose the my antecedent and then bind |Y[n]/X[n]-M/L|<epsilon but I'd have to get there algebraically first.
15. ### Kinda Urgent. Proof Wriiting. Squences

Homework Statement Prove that if X[n]->L, X[n] doesn't equal 0 for all n, L doesn't equal 0 and Y[n]->M, then (Y[n]/X[n])->(M/L). Homework Equations They only give you the squeeze theroem and that if X[n] converges then it's limit is unique. O and the definition. A sequence of reals has...