Weekly Math Problem #72

Limits. I found this week's problem in my personal archives. 😁 I'm inspired by students I'll be working with that are learning limits. I can recall learning the concept of what a limit is and how to evaluate the limit of various types of functions. Honestly, I learned limits more after my Calculus 1 course as tutor than when I was enrolled in the course. Repetition really is the key 🗝 for me. Seriously, if I don't use it, I can definitely lose it. **Whispering** "This is why I started my blog." 😊

To solve this week's problem in completion, you need to recall the following math skills:

        ✔️     Substitution        
        ✔️     Simplifying rational expressions
        ✔️     Web Resource: Limits (Evaluating)

             

WMP! #72 want us to...

Happy solving!

Check back on Saturday, February 5th for the solution, which will be posted below ⬇️.

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✏️📓 Solution Time! 📓✏️

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To begin the process of finding the limit, we'll use the substitution method. 

Unfortunately, the substitution method yields an indeterminate form expression. What does that mean? 🤷🏿‍♀️ This means that the method used doesn't tell us whether or not the limit exists. Another method for evaluating the limit needs to be used to determine whether or not the limit exists.

The numerator of the expression is a cubic polynomial that can be factored. The form is a difference of cubes. When the cubic expression is factored, you will see that one of the factors matches the expression in the denominator. **Yes!** So, we'll simplify the expression. This time, the substitution method will work.

Nice. The limit does exist, and it's equal to 3. 

Another method that can be used to evaluate a limit that yields and indeterminate form is L'Hôpital's Rule. It involves using derivatives and yields the same results. Take a look...

I didn't do it here, but you can graph the original expression and the simplified expression to see what their graphs look like. Then verify that as x approaches 1 from the left and right, the output value is 3.

▪️ Were you able to find the limit?
▪️ Did you do something else to find the limit? If so, please share. (No judgment.)

▪️ Let me know what you thought about this week's problem in the comments section. 

Thank you for solving with me this week. 😊
Up next...WMP! #73. 

Cheers!

The Younge Lady