Consider the following piecewise function f : R^2 + R defined by f(x,y) = { exp(-1/2x^2+3y^2) if (x,y) not equal to (0,0), m if (x,y) = (0,0) Find all values of m that make f a continuous function of R^2.Show that the functi...
Continuity in Piecewise Functions: Continuity at points where the piecewise function changes expression depends on the limit of the function at the point and the value of the function at the point. In this case the side limits are calculated with different functions, o...
Tags Continuity Differentiability Function Piecewise function In either case, you will then need to show that ##\lim_{n\rightarrow \infty} f(x_n) \ne \lim_{n\rightarrow \infty} f(y_n)##, which should be straightforward using the definitions of ##x_n## and ##y_n##.In summary,...
Limits and continuity of piecewise functions. In each case, provide a specific value for a (and a specific value for b, when appropriate) to ensure that each piecewise-defined function is continuous at x=1. The " a " in one pro...
2.Holes in Piecewise Functions: these occur when there is a singularx-value that is not in the domain of the function. 3.Steps in Piecewise Functions: these occur when the endpoints of adjacent branches don’t match up. 4.Toolkit Functions: you must be familiar enough with the elementary ...
Estimates of Functions, Orthogonal to Piecewise Constant Functions, in Terms of the Second Modulus of ContinuityThe paper is devoted to the problem of finding the exact constant W2 in the inequality ‖f‖ ≤ K ω2(f, 1) for bounded functions f with the property∫kk+1f(x)dx=0,k∈. Our...
In this note we propose a finite element method of displacement type for problems in perfect plasticity where we use a finite element space V h of piecewise polynomial functions with no requirement on inter-element continuity. In order... C Johnson,R Scott - Springer Berlin Heidelberg 被引量:...
This means that g is actually continuous at x=0, even though it was cobbled together in piecewise fashion. In the problem of limit, we can substitute the value of x, because the continuity connects the "near" with the "at". For example, ...
We prove that a (globally) subanalytic function which is locally Lipschitz continuous with some constant C is piecewise (globally on each piece) Lipschitz continuous with possibly some other constant, where the pieces can be taken to be subanalytic. We also prove the analogous result for a sub...
Determine whether the piecewise function f(x)= -2x + 3, if x is less than 1; x^2, if x is greater than and equal to 1, is continuous at x = 1 or not by using the definition of continuity. Consider the function f(x) ...