All About Limits
A limit is a fundamental concept in calculus concerning the behavior of functions as inputs approach a particular point. The notation used to express the limit of a function f(x) as x approaches a point a is limx→a f(x).
Limits underpin many calculus concepts, including derivatives and integrals. Understanding limits can help in grasping how functions behave near particular points, which is essential in mathematical analysis and applications.
Example Problem
Evaluate the limit: limx→2 (x² - 4)/(x - 2).
Solution: Observing that direct substitution results in a zero denominator, apply factoring: [(x+2)(x-2)]/(x-2) = x+2 as x ≠ 2. Hence, limx→2 (x+2) = 4.
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