Recent content by math2010

So how does this enable us to show f \notin C^1?

It doesn't seem to change much \frac{(m^2+m)^{\frac{1}{3}} . (1+m^2)^{\frac{1}{2}}}{1+m^2} Should we just add the powers, and what about the terms?

Homework Statement How do I simplify the following \frac{\sqrt[3]{m^2+m} . \sqrt{1+m^2}}{\sqrt{1+m^2}.\sqrt{1+m^2}} The Attempt at a Solution I know that the denominator will be 1+m^2 but I don't know how to simplify the numerator. Can anyone show me how?

I'm sorry, I don't really understand what you mean by saying "they don't involve the sign of xy". Do you mean it will be f_x(x,y) = y?

What do you mean?

ah, you mean f_x (x,y)= \frac{y}{|y|} and f_y(x,y)= \frac{x}{|x|}?

without || it is: So f_x (x,y) = y And I adjust it to \frac{y}{|xy|}. And f_y (x,y) = x so it is \frac{x}{|xy|}. Is this correct? :confused:

Since the derivative of the absolute value function is the function \frac{x}{|x|} (where the denominator isn't zero), I guess the derivatives of f(x,y)=|xy| are f_{x}(x,y)= f_y(x,y)= \frac{xy}{|xy|}. So what does this tell us? :rolleyes:

Well the whole problem says "Show that f \notin C^1 at (0,0)." In my course "f \in C^1" means that "f_x and f_y exist and are continuous". So, I know that f(x, y) = |xy| is differentiable at (0,0). I want to prove that it does not belong to C^1, which is why I tried to show it's not...

Homework Statement Let f(x, y) = |xy|. I want to prove that f is not continuous at (0,0). The Attempt at a Solution To prove that f is not continuous at (0,0) I think I need to show that \lim_{(x, y) \to (0, 0)}|xy| \neq 0 I'm a little confused about the |absolute value|...

What are the two one sided limits? That's what I don't get!

Homework Statement I want to find the limit: \lim_{x\to 0}\frac{sin|x|}{x} The Attempt at a Solution I know that the answer must be "limit doesn't exist" but I don't know how to arrive at that answer. I know that \lim_{x\to 0}\frac{sinx}{x}=1 but apparently it's a very different...

I tried row-reducing it again using Matlab and I still got a zero row: 1 0 0.5 + 0.5i 0 1 -0.5 + 0.5i 0 0 0

Are you sure? Because I used Mathematica to check the reduced row echelon form of this matrix, and it seems the rref has a row of zeros! Also, does the set containing (-1,0.5+0.5i,1) and (1,0,0) span the subspace?

Homework Statement I have the 3x3 matrix C=(1,-1,1; 2,0,1+i; 0,1+i,-1) and I want to find its nullspace (a set of vectors that span that subspace). The Attempt at a Solution So first I have reduced the matrix to row echelon form and I got this matrix: (1,-1,1; 0,1,-0.5+0.5i; 0,0,0)...