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ap calc study guides

๐Ÿ‘‘ย  Unit 1: Limits & Continuity

๐Ÿถย  Unit 8: Applications of Integration

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

1.3 Estimating Limit Values from Graphs

#graphs

#limits

โฑ๏ธย ย 2 min read

written by

Anusha Tekumulla

anusha tekumulla


๐ŸŽฅWatch: AP Calculus AB/BC - Graphical Limits

This topic centers around the difference between the value a function is approaching (limits) and the value of the function itself. Graphs are a great way to help visualize the difference between these two concepts.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2Flimit-graph-example-1.png?alt=media&token=6122a758-df2b-41a3-9848-e08628187d2a

In the graph above, we can show the difference between the value a function is approaching and the actual value of the function. Starting on the left side of the function and moving toward x = 4, we can see that the y value gets closer to y = 5. Starting on the right side and moving backward to x = 4, we also get closer to y = 5. However, if we try to evaluate the function AT x = 4 we get y = 4. This is the key difference between the value a function is approaching and the value of the function itself. In this example, the limit is 5 but the value of f(4) is 4.ย ๐Ÿค“

The big takeaway from this example is that the value of a function at a particular value does not (โœ–) mean that the limit value is the same.

Estimating a Limit Value: Step by Step

As you saw in the example above, we estimate a limit value in a graph by approaching the x value from both sides. Here are the steps needed to estimate the limit value:ย 

  1. First, we approach the x value from the left side.ย 

  2. After getting a y value from the left side, approach the x value from the right side.ย 

  3. If the y values from the left side and the right side are the same, we say that the limit is that y value. If the values arenโ€™t equal, we say that the limit does not exist.ย 

If youโ€™re still confused, take a look at the pictures below.ย ๐Ÿ“ท

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2Fdownload-21.png?alt=media&token=d8c3188c-d729-4237-8567-c8088c663bdf

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2Fdownload-22.png?alt=media&token=8486ce71-040a-4b78-8075-2dc0b904311c

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