Recent content by psycho2499

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. A quick question about Butane as a solvent?

The extracts of different plants.
11. A quick question about Butane as a solvent?

If say cold butane bound to something ( butane as a solvent ) is poured into warm water, then what happens. I don't believe anything will happen except the butane will boil off and what is in the solution will fall off to the bottom till the water is cooled completely but I'm just checkin with...
12. 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...
13. Point P is the intersection of the terminal arm of angle in standard position and th

My teacher used to say that the easiest way to remember sin theta is Y sin
14. Point P is the intersection of the terminal arm of angle in standard position and th

The definition of sin theta in any case is opposite/hypotenuse and cos theta is adjecent/hypotenuse. The unit circle has a radius of 1 so any right triangle with vertices at the origin, a point P on the circle, and the X or Y axis ( is a purely your choice, most choose the X axis ) will have a...
15. 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))...