๐Ÿ“š

All Subjects

ย >ย 

โ™พ๏ธย 

AP Calc

ย >ย 

๐Ÿ‘‘

Unit 1

1.2 Defining Limits and Using Limit Notation

1 min readโ€ขjune 7, 2020

Anusha Tekumulla


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.

Resources:

Was this guide helpful?

Join us on Discord

Thousands of students are studying with us for the AP Calculus AB/BC exam.

join now

Browse Study Guides By Unit

โœ๏ธ
Free Response Questions (FRQ)

๐Ÿง
Multiple Choice Questions (MCQ)

โ™พ
Unit 10: Infinite Sequences and Series (BC Only)

๐Ÿค“
Unit 2: Differentiation: Definition & Fundamental Properties

๐Ÿค™๐Ÿฝ
Unit 3: Differentiation: Composite, Implicit & Inverse Functions

๐Ÿ‘€
Unit 4: Contextual Applications of the Differentiation

โœจ
Unit 5: Analytical Applications of Differentiation

๐Ÿ”ฅ
Unit 6: Integration and Accumulation of Change

๐Ÿ’Ž
Unit 7: Differential Equations

๐Ÿถ
Unit 8: Applications of Integration

๐Ÿฆ–
Unit 9: Parametric Equations, Polar Coordinates & Vector Valued Functions (BC Only)

Play this on HyperTyper

Practice your typing skills while reading Defining Limits and Using Limit Notation

Start Game