ductape
Nov13-11, 01:16 AM
Hello,
I was curious today as to whether or not one can interchange the following integral and limit in general:
\lim_{\epsilon\to 0} \int f(\epsilon x)dx = \int \lim_{\epsilon\to 0} f(\epsilon x)dx
I know that limits and integrals cannot generally be interchanged when the variable of integration is the same as the variable in the limit (in this notation x), but in our case where epsilon is an arbitrary constant and not the variable of integration can this be done?
I was curious today as to whether or not one can interchange the following integral and limit in general:
\lim_{\epsilon\to 0} \int f(\epsilon x)dx = \int \lim_{\epsilon\to 0} f(\epsilon x)dx
I know that limits and integrals cannot generally be interchanged when the variable of integration is the same as the variable in the limit (in this notation x), but in our case where epsilon is an arbitrary constant and not the variable of integration can this be done?