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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 To state a real valued function. The reason for using ap calculus instead of just calculus is to ensure that advanced stuff is filtered out.

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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 But i would be very interested to know the motivation behind the definition of an absolutely continuous function I was looking at the image of a piecewise continuous

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

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 $\mathbb r$. Closure of continuous image of closure ask question asked 12 years, 11 months ago modified 12 years, 11 months ago The containment continuous$\subset$integrable depends on the domain of integration It is true if the domain is closed and bounded (a closed interval), false for open intervals, and for unbounded intervals.

So continuously differentiable means differentiable in a continuous way. 3 this property is unrelated to the completeness of the domain or range, but instead only to the linear nature of the operator Yes, a linear operator (between normed spaces) is bounded if and only if it is continuous. This might probably be classed as a soft question