Recent content by sarahr

perfect example! thankss

If the original graph, f, has a cusp, obviously the derivative is not defined at the x-value of the cusp (resulting in an asymptote). but, what if you are viewing a graph of the derivative, f ', and it has a cusp.. what is going on at the x-value of the cusp on the original graph, f ?

what is the difference between a linear approximation and a tangent line? my understanding is that the linear approximation is that it uses the tangent line at (a, f(a)) as an approximation to the curve y = f(x). my question really is, then why in calculus I do they make an entirely separate...

nevermind! i figured it out! :)

Homework Statement Consider a symmetric matrix, A, n x n with distinct eigenvalues lambda_1 > lambda_2 > ... > lambda_n (note: i didnt miss anything here typing this, there are no absolute values here). What value of the shift beta will give fastest convergence to lamba_1 and its...

this is what I've got going right now: [the previous initial step found above] Assume it holds for all subsets of n elements, and let A = {X1, X2, ..., Xn+1}. By the induction hypothesis, {X1, X2, ..., Xn} has a lub. Call this lub L1. Since {X1, X2, ..., Xn} has a lub, then L1 union...

Homework Statement "Prove that in a lattice (L, <=) every finite nonempty subset S has a least upper bound and a greatest lower bound" Homework Equations The Attempt at a Solution I'm going to try and prove this by induction. For the initial case, show its true for n=2. So take a lattice...

I'm obviously using here that a unitary map M satisfies M*M = I. I didn't realize I could use that for this problem. Then I did and it become much clearer.

I think I'm getting there now. Let U be the collection of unitary maps. I need to show that U is a group under multiplication. 1. the identity is an element of U because: I*I = I , therefore I is an element of U. 2. Let M1, M2 be elements of U. I need to show that M1M2 is an elt. of...

i need to show that the unitary maps form a group under multiplication. I've never had algebra (im in linear algebra) so this is the first time I've seen this idea of 'groups'. i tried to look stuff up, so i think i see now that i need to show: 1) identity is an element 2) if x,y are elements...

oh! this is very clear now. thanks so much! sarah.

no, the question does not say that f(x)<=f(y) (or vice versa.) what is typed between the two lines is the exact question from my text. thanks!

hello, i need to prove: _______________________ if a differentiable function f:(a,b) ----> R (reals) assumes a max or a min at some x element of (a,b), prove that f'(x) = 0. why is this assertion false when [a,b] replaces (a,b)? _______________________ -I'm stumped at where to...