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Unit 1

1.2 Defining Limits and Using Limit Notation

1 min readโ€ขseptember 12, 2021

anusha

Anusha Tekumulla


AP Calculus AB/BCย โ™พ๏ธ

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Defining Limits and Using Limit Notation

๐ŸŽฅWatch: 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: ๐Ÿ“ˆ
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2Fdownload-7.png?alt=media&token=6b23c385-7087-4ed5-bafa-9a15c0d0a180
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, letโ€™s look at the function f(x) = x + 1. ๐Ÿ–‹
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2Fdownload-9.png?alt=media&token=ca3f1e73-3af9-4a88-9592-d3dde788302d
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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