This week in Calc., I learned about the fabulous Chain Rule. This rule is kinda difficult to comprehend at first, but I think I understand the Chain Rule better than when we first started that worksheet. The Chain Rule applies to when you have composite functions, or functions inside of functions. To use the Chain Rule, you take the derivative of the outside functions, but keep the inside function the same, and multiply it by the derivative of the inside function or you could use the equation, f(g(x))=f'(g(x)) x g'(x). The Chain Rule took me some time to get used to and I think it will take me a little longer to understand the more complex problems, but I have the general idea down. The problems I have trouble with are the ones that are when you have to chain the Chain Rule. Luckily, there are several people I know in the class that can help me solidify it. I found it quite cool that we have already been doing the Chain Rule when we do the Power Rule. I’m glad that we learned the Power Rule before the Chain Rule because it is so much shorter than doing the Chain Rule on a simple equation.
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This week in Calculus, we learned the rules for derivatives and an easier way find the derivative. I really wish we learned this trick earlier when we first learned derivatives because it would have saved me so much time and paper. Derivatives have become less terrifying and scary now that we've been doing it on a consistent basis, but then you threw in those anti-derivatives. They are not difficult but when you first said anti-derivatives, I thought, "Dear lord, what the heck is an anti-derivative!" I have since found out that they are not as scary as I originally thought, but if you had taught them on Friday, which was Friday the 13 in the scariest month ever, October, I probably would have thought they were the most terrifying, evil, most difficult thing to do. The only difficult thing about anti-derivatives is remembering to add the +c at the end. Derivatives are easy now that we've had lots of practice on them. I think they're starting to be fun. What have you done to me, calculus shouldn't be fun! I hope the rest of the chapters in this trimester, and the rest of the trimesters this year are just as easy and kinda fun, but not too fun because calculus shouln't be fun.
By doing the activity, it gave me an understanding that we can write the slope using variables, not just points. I mainly struggled with getting the shadow points in because I haven't worked with Desmos before so I had to think about exactly what I wanted. I had to add another shadow point to my second graph and adjust the equation to draw the line between the two shadow points. For the graph that I created, all I had to do was change the original equation that the shadow points follow. This is the case because my other equations could work for any graph because of how they were written. By looking at the slopes of the secant lines, we can have a pretty good idea of what the slope of the tangent line will be.
This week in AP Calc, we learned about Continuity and Salt and Pepper Graphs. Continuity was not that hard because we had gone over it in Pre Calc, but I had never done Salt and Pepper Graphs. Completely new topic to me and it seemed confusing at first, but by the end of the week, I think I understood them. Basically, all a salt and pepper graph is, is a graph of two functions, one of values that are rational, and one of irrational numbers. When the two graphs intersect, there is a limit because it can pass the vertical line test. I thought I was gonna have difficulty with this at first, and the packet seemed intimidating because it looked like it had a lot of explanations like it was gonna be difficult to understand. I was wrong. After working with my table through the problems, I think we all came out understanding the graphs and how they worked. When one person didn't understand something, someone else had an idea on how to solve our problem. Working with the table really helped reinforce the information in my head because I can remember teaching it to someone.
This week in calculus we learned about limits. It took a minute or two for me to remember doing them in Pre-Calc but it came back to me fast. My initial thought when I found out that we were gonna start with limits was, “Limits are super easy, why are we starting with those?” Once I started doing the homework however, I really had to think back to my prior knowledge on how to do limits. I really enjoy limits now because there isn't a lot of work that needs to be done once you know what you’re doing. I think that limits are pretty easy, because you can see where the line is going and can figure out what the limit is. I did learn how to solve limits algebraically, which I don't remember doing in Pre-Calc. I found solving it algebraically was sometimes kinda fun, and having fun doing math is something that doesn't happen often for me. I feel prepared for the next part of the chapter and I believe that those cobwebs in my head are starting to get cleaned off. I look forward to another good week and hope it goes as smoothly as the last two.
This week was actually a lot of fun for the first week. I enjoy the environment and the people in the class which will make it easier to learn. , but as usual when coming off of a three month break, I did not remember anything from the previous year. This of course makes learning anything new difficult as I no longer had the base to work off of. I think that the review packet that we were given at the beginning of the year was very helpful because it was a mini refresher course of Pre-Calculus. The packet really helps because it helps build that ground level of knowledge back up to the level it was at the end of last year. It helped ease me back into the routine of doing math again. I will admit that I struggled with the packet for the first couple days, but after talking with the people around me, I am feeling better about what knowledge I need to begin learning new topics in this class. I now feel better about doing all the topics outlined in the packet. It was an amazing first week and I hope the rest of the weeks are just as fun.
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February 2018
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