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leanprover-community.github.io | ||
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mathscholar.org
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| | | | | [AI summary] The text presents a detailed, self-contained proof of the Fundamental Theorem of Calculus (FTC) using basic principles of calculus and real analysis. It breaks the proof into two parts: Part 1 establishes that the integral of a continuous function defines a differentiable function whose derivative is the original function, and Part 2 shows that the definite integral of a continuous function can be computed as the difference of an antiderivative evaluated at the endpoints. The proof relies on lemmas about continuity, differentiability, and the properties of integrals, avoiding advanced techniques. The text is structured to provide a clear, step-by-step derivation of the FTC for readers familiar with calculus fundamentals. | |
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kndrck.co
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| | | | | Prelude State monads, introduced to me during the data61 functional programming course was one of my most memorable encounter with a monad. This was mainly because things only started to clicked and made a tiny bit of sense after a couple of weeks of frustration. This article is my attempt to explain the underlying mechanics of the State Monad to try and relief the frustration of whomever who was in my position. | |
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thehousecarpenter.wordpress.com
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| | | | | As usual, this post can be viewed as a PDF. Theorem (Boundedness Theorem). A continuous real-valued function on a closed interval is bounded. Proof. Suppose f is such a function and [a,?b] is its domain. First, observe that for every c?[a,?b], since f is continuous at c, there is a positive $latex \delta \in {\mathbb... | |
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scenesfromthemorgue.wordpress.com
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