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Unit 1

1.7 Selecting Procedures for Determining Limits

#limits

#methods


written by

Anusha Tekumulla

anusha tekumulla

published on march 25, 2020

Last updated on June 7, 2020

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Selecting Procedures for Determining Limits

๐ŸŽฅWatch: AP Calculus AB/BC - Algebraic Limits

In this topic, we will discuss how to choose a method to determine a limit. So far, weโ€™ve learned about multiple ways to determine limits: direct substitution, factoring, and trigonometric identities. But how will you know when to use each of them? Take a look at the flowchart below to better understand when to use each method.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2Fa193121287b64721de28fcbfaec9f5919a367dd2.png?alt=media&token=bb901189-74a9-4eeb-9c6c-90ec09680be5

Khan Academy

As we discussed before, the first thing you should do is use direct substitution. This is the easiest and simplest way to determine a limit. While you might be able to solve a limit using a more complicated method, you should always try to use direct substitution first.ย ๐Ÿ•ต

As the flowchart states, you can get three outcomes with direct substitution:ย 

  1. If you use direct substitution and you get a number, this is most likely the limit. However, you should still look at the graph of the function around the x value to be sure.ย ๐Ÿ’ฏ

  2. If you get b/0 when using direct substitution and b isnโ€™t 0, then you most likely have an asymptote. After confirming that there is an asymptote, you can conclude that the limit does not exist.ย โœ–

  3. If you get 0/0, you have an indeterminate form and you must use either factoring, conjugates, or trig identities to solve the limit. Remember that indeterminate forms are things like 0/0 or โˆž/โˆž.ย โ˜‘

If after trying factoring, conjugates, or trig identities you still cannot come up with an answer, the best thing to do is approximate the limit.ย ๐Ÿ‘Œ

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