Homework Statement Determine the limit l for a given a and prove that it is the limit by showing how to find δ such that |f(x)-l|<ε for all x satisfying 0<|x-a|<δ. f(x)=x^{2}, arbitrary a.Homework Equations I will incorporate the triangle inequality in this proof.The Atte...
What about the other sides of the original triangle? Do we get a map like the first picture below (which is how I understand the construction), or like the second picture (which would make more sense)? Again, I can't solve the exercise. I can prove that ther...
Learn the meaning of delta symbol and how the Greek letter delta is defined in math and science. See the different uses of capital and lowercase...
Form solid state physics, we know that the volume of k-space per allowed k-value is ##\triangle{\mathbf{k}}=\dfrac{8\pi^3}{V}## ##\sum_{\mathbf{k}}F(\mathbf{k})=\dfrac{V}{(2\pi)^3}\sum_{\mathbf{k}}F(\mathbf{k})\triangle{\mathbf{k}}##... ...
Math Mathematical proofs Let \displaystyle{ f(x) = \begin{cases} 2x, & x \neq 3, \ 13, & x =3. \end{cases} } ...Question:Let f(x)={2x,x≠3,13,x=3.Use an ϵ−δ proof to prove that limx→3f(...
A geodesic triangle Δ(x,y,z) with internal points mx,my and mz and internal distances αx,αy and αz labelled Full size image Definition 1 Let (X, d) be a geodesic metric space, and δ≥0. X is δ-hyperbolic (equivalently, the hyperbolicity of X is δ) if the insize of eve...
Can you always put numbers directly into an expression which has the delta triangle against its variables? For example Faraday's Law is always shown with the delta triangle on top and bottom yet these are dropped when you use it for calculations; which leaves me wondering why they are there...
Forum: General Math P Mutlivariable Epsilon Delta Proofs Like many people on this forum, i am seemingly having a lot of trouble grasping the concepts of Epsilon Delta proofs and the logic behind them. I have read the definition and i realize for e>0 there is a d>0 such that... 0...