⏱️ **2 min read**

#limits

#methods

table of contents

written by

anusha tekumulla

published on march 25, 2020

Last updated on June 7, 2020

🎥**Watch: AP Calculus AB/BC - ****Algebraic Limits**

In this topic, we will discuss how to choose a method to determine a limit. So far, we’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.

**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. 🕵

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

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. 💯If you get

**b/0**when using direct substitution and**b isn’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**. ✖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**∞/∞.**☑

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**. 👌

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