Recent content by PhysicsDude1

Ok, so I've, actually it was you guys, come up with this so far : |√x - √a| < ε ⇔ |√x - √a| = |√x - √a| . \frac{|\sqrt{x}+ \sqrt{a}|}{|\sqrt{x}+ \sqrt{a}|} ⇔ |√x - √a| = \frac{|x-a|}{|\sqrt{x}+ \sqrt{a}|} ⇔ \frac{|x-a|}{|\sqrt{x}+ \sqrt{a}|} < ε ⇔ |x-a| < ε . |\sqrt{x}+...

|√x - √a| < ε ⇔ Sorry, accidentally clicked on post. I'm working on it :p

Thank you. This was very helpful intuive-wise! But how do I do this formally? Do I write δ in terms of ε? I'm sorry but I'm really stuck here.

Homework Statement Prove that \sqrt{x} is continuous in R+ by using the epsilon-delta definition. Homework Equations A function f from R to R is continuous at a point a \in R if : Given ε> 0 there exists δ > 0 such that if |a - x| < δ then |f(a) - f(x)| < ε The Attempt at a...

I'm sorry, I meant orthogonal coordinate system :) Basically I'm trying to find G' which is the metric of the coordinate system (X', Y'). There are 2 ways to find this : 1) G' = M^T * G * M (M=inverse transformationformula // M^T = the transposed matrix of M // G = metric of the...

If there's something confusing, just ask :)

Also, I can't fall asleep because of this. I REALLY want to know the answer :p

Homework Statement For the orthonormal coordinate system (X,Y) the metric is \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} Calculate G' in 2 ways. 1) G'= M^{T}*G*M 2) g\acute{}_{ij} = \overline{a}\acute{}_{i} . \overline{a}\acute{}_{j} Homework Equations \begin{pmatrix}...