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What is the definition of lim f(x)?

What is the definition of lim f(x)?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Topic: Understanding Limits in Calculus** **Question: What is the definition of \(\lim_{x \to a} f(x)\)?** In calculus, the notation \(\lim_{x \to a} f(x)\) represents the limit of the function \(f(x)\) as \(x\) approaches the value \(a\). The limit is the value that \(f(x)\) gets closer to as \(x\) approaches \(a\) from both the left and the right. This concept is fundamental to the understanding of continuity, derivatives, and integrals in calculus. Understanding limits is crucial for analyzing the behavior of functions at specific points or as they approach infinity. Limits help resolve indeterminate forms and are instrumental in defining the derivative of a function. For a more in-depth exploration, let's delve into the formal definition and how limits can be evaluated in different mathematical contexts.
Transcribed Image Text:**Topic: Understanding Limits in Calculus** **Question: What is the definition of \(\lim_{x \to a} f(x)\)?** In calculus, the notation \(\lim_{x \to a} f(x)\) represents the limit of the function \(f(x)\) as \(x\) approaches the value \(a\). The limit is the value that \(f(x)\) gets closer to as \(x\) approaches \(a\) from both the left and the right. This concept is fundamental to the understanding of continuity, derivatives, and integrals in calculus. Understanding limits is crucial for analyzing the behavior of functions at specific points or as they approach infinity. Limits help resolve indeterminate forms and are instrumental in defining the derivative of a function. For a more in-depth exploration, let's delve into the formal definition and how limits can be evaluated in different mathematical contexts.
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