Recent content by cappygal

Thank you so much .. it actually makes sense now .. Something about being out of school with a broken pelvis means that it's harder to understand what they do in class without you ... thanks!

How do I prove the linear independence of the standard basis vectors? My book is helpful by giving the definition of linear independence and a couple examples, but never once shows how to prove that they are linearly independent. I know that the list of standard basis vectors is linearly...

I thought when you were using definition of derivitive, you aren't allowed to plug in for a until you have it simplified? Am I wrong? I could be .. it's been a year since I've had to work with definition of derivative.

wow! I am having a major brain fart here .. I'm in multivariable calc but I need to take the derivative of a single variable function using the definition of derivative. The function is: f(x)=abs(x)^(3/2) and I need to find the derivative when a=0 so by the def of derivative, the...

I need to find the limit as x,y->0 of (x^2+y^2)(ln(x^2+2y^2)) anylitically. since the limit of this is 0(-infinity) which is indeterminant .. I tried to approach it along the line y=x which gives: lim(x->0) of [2x^2*ln(3x^2)]. Again, that gives 0(-infinity). Now, I haven't done calculus in 6...

I need to find a value for f at (0,0) to make this function continuous: f(x,y)=sqrt(x^2+y^2)/[abs(x) + abs(y)^(1/3)] With other functions in this problem I simply took the limit .. but taking the limit gives 0/0. In single-variable calculus I would apply l'hopital's rule to this, but I'm...

For a sequence a_1, a_2, ... in R^n to be convergent there are (at least) 2 theorems, as follows: if for all epsilon>0 there exists an M such that when m>M, then |a_m-a|<epsilon and also: If u(epsilon) is a function such that u(epsilon)-->0 as epsilon-->0, then the sequence is...

clarification It is a purely abstract situation. The book says: "Prove the following statements for open subsets of R^n (where R is the Reals): a) any union of open sets is open. b) A finite intersection of open sets is open c) An infinite intersection of open sets is not necessarily open...

In my multivariable calc class, we're asked to prove that the finite intersection of open sets is open. I've tried to find help on the internet but couldn't find anything to help. I understand somewhat the idea of "nesting sets" that some proofs use .. can anyone help me understand this to prove...