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1.2 Defining Limits and Using Limit Notation

1 min readβ€’february 15, 2024


AP Calculus AB/BC ♾️

279Β resources
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Defining Limits and Using Limit Notation

πŸŽ₯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: πŸ“ˆ
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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, let’s look at the function f(x) = x + 1. πŸ–‹
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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.
Browse Study Guides By Unit
πŸ‘‘Unit 1 – Limits & Continuity
πŸ€“Unit 2 – Fundamentals of Differentiation
πŸ€™πŸ½Unit 3 – Composite, Implicit, & Inverse Functions
πŸ‘€Unit 4 – Contextual Applications of Differentiation
✨Unit 5 – Analytical Applications of Differentiation
πŸ”₯Unit 6 – Integration & Accumulation of Change
πŸ’ŽUnit 7 – Differential Equations
🐢Unit 8 – Applications of Integration
πŸ¦–Unit 9 – Parametric Equations, Polar Coordinates, & Vector-Valued Functions (BC Only)
β™ΎUnit 10 – Infinite Sequences & Series (BC Only)
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