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Likewise, a limit helps us to understand the idea of closeness and approximation and is the foundation for definitions such as continuity, differentiation, and antidifferentiations (i.e., integrals). And here’s the best part, this cornerstone topic is easy to understand and master because the ...
Definite integrals are a type of integral wherein the integration is done within a defined interval. The interval can be either open or closed, as long as one is present. Unlike indefinite integrals, where the answers are functions, the answers to definite integrals have actual values. The int...
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In a calculus course, derivatives and integrals tend to steal the show, and rightfully so— they have a wide variety of applications in the physical and social sciences. However, these two fundamental ideas are rooted in one idea, that of limits. Sequences and series are essentially about lim...
As we will argue, the presence of black hole soft hair is indeed sufficient to avoid the conclusion that infalling observers must experience a firewall. 1.1 Argumentation We start with an outline of our reasoning for why the HPS proposal invalidates the AMPS conclusion. 1. Firewall argument ...
15.2 Limits 15.2.1 Introduction to Limits 15.2.2 Definition 15.2.3 Big O Notation 15.2.4 Change of Variable 15.2.5 One-sided Limits 15.3 Differentiation (permaquestions: 15.3.26 15.3.27) 15.3.1 Instantaneous Rate of Change 15.3.2 Derivatives of Specific Functions 15.3.3 Rules 15.3.4 Implicit...
We call ρ(t) the neural response function and use it to re-express sums neural response function ρ(t) over spikes as integrals over time. For example, for any well-behaved function h(t), we can write n i=1 h(t −t i ) = T 0 dτ h(τ)ρ(t −τ) (1.2) where the ...