This week in calc we took our study of derivatives a few steps further. Starting out we learned a much less time consuming and tedious way to take the derivative of a function. You can find the derivative by multiplying the coefficient of a term in a function by its exponent and subtracting one from the exponent in each term of a function. This technique has sped up the process so much that doing more complex problems is much less intimidating. We also learned how to take anti derivatives of a function, which is just the process explained about and adding +c at the end. This lesson had made calculus as a whole much less intimidating to me as I find my rhythm in this class for the year. To end the week it felt like I was transported back to precalc as we looked at derivative rules for trig functions. I personally enjoy looking at and using trigonometric identities and today's lesson for once made a lot of sense right off the bat.
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At the begining of this assignment the idea that a single point can have a slope was really abstract to me, even with begining of class assignment I still found it strange but began to grasp the concept. I had zero idea how to even begin the project, but that's not uncommon, usually it takes at least a one on one conversation with someone and like 5 more examples before I grasp any math concept. However, I was not the only one in class who was struggling and after asking Mr.Cresswell for help I was on the right track. The best way to start was to draw out everything on paper and look at things that way before trying to put anything into desmos. To transition from the first graph to the second graph
This week we continued discussing limits. In order to look deeper into the topic we discussed limits approaching infinity as well as the continuity and discontinuity of a function. While I know what we are learning admittedly I am not the most comfortable with the subject matter as I have missed a lot of class this week due to other school activities. I managed to grasp the concept that a limit approaching infinity describes a limit as a function moves farther right on the number line or farther left in the case of negative infinity. In the case of the continuity of a limit I have a basic grasp of the concept however I still struggle with differentiating between the different kinds of discontinuity. A Function is continuous when the function and the limit have the same value, and discontinuous when it is not. I tend to understand a concept better after looking at multiple examples and reading information written different ways, so I often look up topics online again once I get home to refresh the information again. This week I used http://tutorial.math.lamar.edu/Classes/CalcI/Continuity.aspx for a diffent angle while working on assignments.
This week we took our first assessment and began learning about Limits. After taking the prerequisite assessment I have learned that I need to put effort into showing my work. Often when forced to show work I have been in the habit of skipping steps and bluffing my way through problems. This year I plan on putting extra energy into thinking about why math equations work the way they do and how to solve them algebraically as opposed to the graph and hope for the best strategy I have been going with. Also this week we dove back into limits, which is familiar to me as I learned about them last year in my Honors Pre Calculus class. To be completely honest both times I have sat through a lesson on limits I could not for the life of me tell you what greater purpose they serve in math and calculus, so I read this while writing this to attempt to remedy that. I assume this means that the next step forward in this class will be studying derivatives. I enjoy that the first lesson in the class was something I had already done so that I could more easily use it as a way to practice focusing more on solving things algebraically.
This week I struggled a lot. I realized that I have an incredibly hard time doing math without some sort of crutch. Since the beginning of my high school math journey, I have always had access to two things: a calculator and a detailed book of notes. Once I looked at the prerequisite packet I remembered talking about all the topics included, but I did not remember how to do them, like, at all. I could remember what page those topics might have been on in my notebook or in the textbook but I could not even remember how I might start actually solving the problem. This made me realize something about how I've been treating my schooling, I've been memorizing not learning. I don’t want to say that the first week of class made me feel bad about myself, but it was kind of infuriating to start an assignment on subject matter that I spent a whole year prior learning about and find myself hitting a wall every time I try to start a problem. However, through the course of the week I found that my tablemates where going through similar things. Though our collective suffering we managed to talk through our struggles and share old notes and tips from when we were in math class together last year.
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January 2018
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