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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 Here you want to refer to the topology of the latter as a normed space, which does not depend on the norm since they are all equivalent in finite dimension. · in my mind it seems to say, if a function is continuous, we can show that if it is also differentiable, then it is continuous. 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) … Can you think of some compact sets in $\mathbf r$? · to understand the difference between continuity and uniform continuity, it is useful to think of a particular example of a function thats continuous on $\mathbb r$ but not uniformly … Are continuous … · basic real analysis should be a source of at least some intuition (which is misleading at times, granted). · closure and continuous map ask question asked 6 years, modified 6 years, Whats reputation … · 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. Then the determinant is a polynomial in … Rather than what i was expecting, namely, if a function is … The authors prove the proposition that every proper convex function defined on a finite-dimensional separated topological linear space is continuous on the interior of its effective domain. Upvoting indicates when questions and answers are useful. · youll need to complete a few actions and gain 15 reputation points before being able to upvote. I was looking at the image of a …