Weekly Math Problem! #1

It's SPRING! It's been spring for over a month now, so it's about time I get these problems going. (I know..I know...it's been a long wait. However, I have an excuse. It's the same as everybody else....and you know what it is. 👀) For a little more info on these problems, check out my previous post. As promised, The Younge Lady's weekly math problems are here! So, without further ado, here is WMP #1:

Limits Involving Trigonometric Functions. This week's question came from a tutoring session that happened a couple months ago and is typically learned in a Calculus I course. To solve it in completion, you need to recall the following math skills:

     ✔️  How to deal with fractions 
     ✔️  How to deal with trigonometric functions 
     ✔️  Limit properties
     ✔️  Finding derivatives of trigonometric functions 

I will say that there are two ways to do this problem. Ready?

Happy solving! Check back on Friday, May 8th for the solution, which will be posted below ⬇️.

Shameless plug: Follow me on Instagram @TheYoungeLady

✏️📓 Solution Time! 📓✏️

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As previously mentioned, there are two ways to find this limit. The first method is algebraic in nature; it is not necessary to know derivatives to find this limit. Limits are most often taught before derivatives are, so algebraic methods are explored. Once derivatives and other topics have been taught, limits are re-explored at some point and the method of L'Hôpital's rule is used to evaluate limits that yield indeterminate forms when evaluated at the specified value.

Algebraic Method

L'Hôpital's Rule Method

That's pretty much it. Two different methods, same answer. That's one of my favorite things about mathematics--one problem can be solved multiple ways. 

◾️ Did you arrive at the same answer I have above?? 

◾️ How did you find the limit?? 

◾️ When was the last time you did a limit problem??

◾️ Comment below with your responses and let me know what you thought about this week's problem.

Cheers!

The Younge Lady