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# 1.2 Defining Limits and Using Limit Notation

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## Defining Limits and Using Limit Notation

π₯Watch: AP Calculus AB/BC - Graphical Limits
A limit is the y value a function approaches as it approaches a certain x value. You will usually see limits in this notation: π
Calcworkshop
This means that as x approaches a, on the graph of f(x), the value on the y-axis that the function approaches is L.
To understand limits better, letβs look at the function f(x) = x + 1. π
GraphSketch
The limit of f(x) as x approaches 4 is the value f(x) approaches as we get closer and closer to x = 4. If we were to graph f(x), this is the y-value we approach when we look at the graph of f(x) and get closer and closer to the point on the graph where x = 4.
For example, if we start at the point (1, 2) and move on the graph until we get really close to x = 4, then our y-value gets really close to 5. Similarly, if we start at (6, 7) and move closer to x = 4, the y-value gets closer and closer to 5. Thus, the limit of f(x) as x approaches x = 4 is 5.
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πUnit 1 β Limits & Continuity
π€Unit 2 β Fundamentals of Differentiation
π€π½Unit 3 β Composite, Implicit, & Inverse Functions
πUnit 4 β Contextual Applications of Differentiation
β¨Unit 5 β Analytical Applications of Differentiation
π₯Unit 6 β Integration & Accumulation of Change
πUnit 7 β Differential Equations
πΆUnit 8 β Applications of Integration
π¦Unit 9 β Parametric Equations, Polar Coordinates, & Vector-Valued Functions (BC Only)
βΎUnit 10 β Infinite Sequences & Series (BC Only)
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