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 $\mathbb R$ but not uniformly continuous on $\mathbb R$.
Are all continuous functions also absolutely continuous functions or not? If it does, then does its inverse hold? Kindly give an example?
If f is differentiable at a point x, then f must also be continuous at x, locally linear (the reverse does not hold). If f is even not differentiable at a point x, how it could be as much as continuous derivative there.
Basic real analysis should be a source of at least some intuition (which is misleading at times, granted). Can you think of some compact sets in $\mathbf R$? Are continuous functions on those sets uniformly continuous? Can you remember any theorems regarding those? Another idea is to start to try to prove the statement and see whether things start to fall apart.
Both discrete and continuous variables generally do have changing values—and a discrete variable can vary continuously with time. I am quite aware that discrete variables are those values that you can count while continuous variables are those that you can measure such as weight or height.
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
real analysis - How to show a function is absolutely continuous ...
If you've learned that continuous functions on compact sets are uniformly continuous, then this turns out to be a simple exercise with the extended real numbers.