The continuous extension of f(x) f (x) at x= c x = c makes the function continuous at that point. Can you elaborate some more? I wasn't able to find very much on "continuous extension" throughout the web. How can you turn a point of discontinuity into a point of continuity? How is the function being "extended" into continuity? Thank you.
A continuous function is a function where the limit exists everywhere, and the function at those points is defined to be the same as the limit. I was looking at the image of a piecewise continuous
12 Following is the formula to calculate continuous compounding A = P e^(RT) Continuous Compound Interest Formula where, P = principal amount (initial investment) r = annual interest rate (as a decimal) t = number of years A = amount after time t The above is specific to continuous compounding.
To understand the difference between continuity and uniform continuity, it is useful to think of a particular example of a function that's continuous on R but not uniformly continuous on R.
Is the derivative of a differentiable function always continuous? My intuition goes like this: If we imagine derivative as function which describes slopes of (special) tangent lines to points on a ...
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Since the Sobolev space only cares about function up to a set of measure zero, we could ask questions about whether functions in the space are continuous, strongly differentiable, etc., but those questions are not invariant under modifications on a set of measure zero, so they can only be answered by seeing if there are sufficiently smooth ...
A function is "differentiable" if it has a derivative. A function is "continuous" if it has no sudden jumps in it. Until today, I thought these were merely two equivalent definitions of the same c...
I was reading through Munkres' Topology and in the section on Continuous Functions, these three statements came up: If a function is continuous, open, and bijective, it is a homeomorphism. If a
Are there any examples of functions that are continuous, yet not differentiable? The other way around seems a bit simpler -- a differentiable function is obviously always going to be continuous.
