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- What is a continuous extension? - Mathematics Stack Exchange
To find examples and explanations on the internet at the elementary calculus level, try googling the phrase "continuous extension" (or variations of it, such as "extension by continuity") simultaneously with the phrase "ap calculus" The reason for using "ap calculus" instead of just "calculus" is to ensure that advanced stuff is filtered out
- Proof of Continuous compounding formula - Mathematics Stack Exchange
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 - Continuous image of compact sets are compact . . .
The fact that f is continuous doesn't guarantee that the image of f's inverse is open, much less is even defined For example, f (x) = 1 is continuous but it's inverse isn't even defined Maybe the argument here needs to be broken into more cases?
- is bounded linear operator necessarily continuous?
In general, is a bounded linear operator necessarily continuous (I guess the answer is no, but what would be a counter example?) Are things in Banach spaces always continuous?
- Must probability density be continuous? - Mathematics Stack Exchange
From other materials that I've read, the probability density of a continuous random variable must itself be continuous Is this correct? If it is, I don't understand why that would be so, why can't
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