Recent content by tracedinair

Alright, AN^(β) = AN^(β-1)T^(1-β) N^(β) = N^(β)N^(-1)TT^(-β) 1 = N^(-1)TT^(-β) N = TT^(-β) Still getting the same thing.

Homework Statement Solve for N: AN^(β) = AN^(β - 1)T^(1-β) Homework Equations The Attempt at a Solution Here's what I got: AN^(β) = AN^(β - 1)T^(1-β) AN^(β) = AN^(β)N^(-1)T^(1)T^(-β) AN^(β) = AN^(β)T / NT^(-β) NAN^(β) =AN^(β)T / T^(-β) N = T/T^(-β)

I got it from my textbook, actually, haha.

Homework Statement Let the symmetric derivative of f at x be lim h->0 f(x+h) + f(x-h) - 2f(x) / h, provided the limit exists. Prove there exists a point, x, in (0,1) where the ordinary derivative exists. Note: f is cont. on [0,1], and the symm. deriv. exists everywhere on (0,1). Prove...

Alright, thank you.

If f'(x) = 1/(1+x) then f(x) = ln(x+1)?

So I took f'(x) = 1 - x + x^2 - x^3 + ... so, the endpoint is going to look like x^(n+1)? I need a formula for the value at the right hand endpoint..would that work?

Homework Statement Find the radius of convergence of \sum n=1 to ∞ of [(-1)^(n-1) x^(n)/(n)] and give a formula for the value of the series at the right hand endpoint. Homework Equations The Attempt at a Solution Not really sure how to start this. I know I'm supposed to use the...

Homework Statement Let lim n-> ∞ a_n = L. Then, let f(x) = ∑ from n=0 to ∞ of (a_n)(x^n). Show that the lim x-> 1 (1-x)f(x) = L. Homework Equations The Attempt at a Solution This one is pretty far over my head. I know at some point you're supposed to use Abel/SBP, but here is what I have so...

Homework Statement Let some function, called f(u,v), be a differentiable function. Then, let its first partial with respect to u = 0 in some region, A. Then, for any u in the region A, f(u,v) will always equal itself for, let's say, f(ui, v) = f(uj, v). Homework EquationsThe Attempt at a...

How are you getting the lim inf and lim sup vales out of (3n+1 + 2n+1)/(6(3n + 2n))?

From my notes: After writing down a formula for {a_n}, describe {a_n} when n is even (n=2k) and when n is odd (2k-1).

Yeah, both cases positive and negative.

The second part of the problem says I should consider both cases, positive and negative, when computing the lim inf and lim sup. I've never seen this type of problem before and I'm totally sure what it is asking me to do.

Homework Statement Given the sequence, 1/2 + 1/3 + 1/(2^(2)) + 1/(3^(2)) + 1/(2^(3)) + 1/(3^(3)) + ..., Describe the terms of the sequence and use it to compute the lim inf (a_n+1)/(a_n); lim sup (a_n+1)/(a_n); lim inf (a_n)^(1/n); lim sup (a_n)^(1/n). Homework EquationsThe Attempt at a...