Here are some properties you will find very helpful when finding limits:

We won’t go each problem step by step because each problem is different from the other, but we will have two examples to show different types of advanced limits that use multiple ways to solve them.

Here’s the first example (click here):

In this example we use the algebraic property and the algebraic limit theorem to get the function in a form, where we can apply L’Hopital’s rule and find the limit.

Here’s the last example (click here):

In this example, we use the algebraic limit theorem to get the function in a form where we can apply the squeeze theorem and find the limit.

In order to solve these advanced limits it is important that the different methods and properties are fresh on your mind. Since there is no exact recipe on how to solve each advanced limit problem because each problem is different, I will tell you what I found easiest for me.

Leah’s Advice:

- Memorize all the different ways to solve a function, such as substitution, factoring, L’Hopital, the chain rule, etc.
- I recommend making flash cards
- It will be a pain to keep flipping through your notes to remember what each method is
- Practice the methods
- Practice problems for each method until you are a pro at solving them
- This goes along with memorization, you want to memorize how use each method
- Practice makes perfect!

Until next time,

Leah

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