Weekly Math Problem #73

Exponents. I found this week's problem on the internet. 👍🏿 We'll be working with exponents this week. For some, working with exponents isn't a big deal. For others, it's confusing/annoying, and I can understand why. No judgment here. So let's take it back to simplifying rational expressions, where the answer should have *positive exponents only*.

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

        ✔️     Properties/Laws of exponents        

             

WMP! #73 want us to...

Happy solving!

Check back on Saturday, February 12th for the solution, which will be posted below ⬇️.

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✏️📓 Solution Time! 📓✏️

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One of the cool things about math is...there is more than one way to simplify or solve something. 

When I looked at this week's problem, I realized that there were multiple ways for me to use the exponent rules to simplify the rational expression. I settled on the one below. I color-coded it so that it would be easier to follow.

First, I went inside the parentheses and used the rules to ensure that I had positive exponents. (Having a negative coefficient is fine.) Then I used my skills to deal with the negative exponent on the outside of the expression. Lastly, I "distributed" that outer exponent to every portion of the rational expression and completed my simplification. 

I used five different exponent rules to simplify this rational expression. 👩🏿‍🏫

▪️ Were you able to simplify the expression?
▪️ If so, did you do it a different way?

▪️ 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! #74. 

Cheers!

The Younge Lady

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 ⬇️.

Shameless 🔌 Plug: Follow me on Instagram @TheYoungeLady
Buy Me a ☕️ Coffee: TheYoungeLady ( I'm gonna need it this year. 😆 )

✏️📓 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

Weekly Math Problem #51

Differentiation. Coming back to a calculus classic this week--the derivative! I feel like calculus helps my mind to feel nice. 😌

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

        ✔️     How to find the derivative of a polynomial

WMP! #51 says...

Happy solving!

Check back on Friday, May 28th for the solution, which will be posted below ⬇️.

Shameless 🔌 Plug: Follow me on Instagram @TheYoungeLady
Buy Me a ☕️ Coffee: TheYoungeLady ( I'm gonna need it this year. 😆 )

✏️📓 Solution Time! 📓✏️

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We've been asked to find the derivative of a polynomial written in product form. This lends itself very easily to the product rule for differentiation. (Also, this is the way to do it because, expanding the polynomial is too time consuming. 😩) This requires us to identify the factors of the polynomial so that we can tag them accordingly. The formula below has f and g in it but, other identifiers can be used. After identifying the factors, I find the derivative for each one, then plug in all components into the formula.

As soon as you complete the substitution, you have found the derivative. The remaining work that's done is for simplification and better presentation of the derivative. 

▪️ Were you able to find the derivative??

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

Thanks for solving with me this week!

Up next, WMP! #51. 👍🏿

Cheers!

The Younge Lady