Recent content by JJ6

Homework Statement I need to find the limit of the sequence: [(1+1/n)(1+2/n)(1+3/n)...(1+n/n)]^(1/n) as n approaches infinity. I know that the limit should come out to 4/e, but I cannot figure out why. Homework Equations None. The Attempt at a Solution The original sequence...

I1/I2 = 25 A1/A2 = 5 Amax = A1 + A2 = 6, Amin = A1 - A2 = 4 Imax/Imin = (6/4)^2 = 9/4 Is this correct?

Homework Statement Hey guys, I'm working on a problem with a double slit electron diffraction experiment. There is a beam of electrons shooting through two slits onto a screen. When only slit 1 is open, the number of electrons hitting the screen is 25 times the number of electrons hitting...

Oh, I finally understand this. I got the recursion to work out fine, and I managed to find the signs of the eigenvalues. Thank you very much, everyone.

OK, the original matrix will have determinant zero when n is odd. If n is even, det(A) = (-1/2)^n. So if n is even, we'll have n roots that are either odd or even, and if n is odd, we'll have n-1 roots that are either even or odd. Then can I say that if λ is a solution, -λ is a solution also...

OK, I'm guessing from what you guys are saying that I need to use Decartes' rule of signs, but I'm not quite sure how I need to apply it. Assuming that I have a polynomial of degree n with all real roots, I should have number of positive roots + number of negative roots + multiplicity of 0 = n...

I have a quick question. If we have n = 2, then the matrix (after subtracting λ*I) has top row [-λ 1/2] and bottom row [1/2 -λ]. Then the characteristic equation is: λ^2 - 1/4 = 0 But in this case, λ could be either positive or negative, right? If these λ that can be either + or - pop up...

I've been trying to come up with a "clever" solution for a while, but to no avail. In my book, we have the theorem: Let A be a matrix, and let its eigenvalues all be real numbers. Then A is diagonalizable if and only if the geometric multiplicity of each eigenvalue equals its algebraic...

If I apply row/column operations on the matrix, will the eigenvalues be the same for the original matrix as they are for the echelon form?

Homework Statement Hey guys, for my linear algebra class I need to find the signs of the eigenvalues (I just need to know how many are positive and how many are negative) of an nxn matrix with zeros everywhere except for the two diagonals directly above and directly below the main diagonal...

So does that mean that d/dx of the integral from -pi/2 to x of sqrt(cost)dt = sqrt(cosx)? Does the -pi/2 just disappear because it is a constant?

Homework Statement Find the arclength of the curve given by y= integral from -pi/2 to x of sqrt(cost)dt. X is restricted between -pi/2 and pi/2. Homework Equations L = Integral from a to b of sqrt((dy/dx)^2 + 1)dx L = Integral from a to b of sqrt((dy/dt)^2 + (dx/dt)^2)dt The...