The activity at the beginning of the hour did not help my understanding in the gif project because I was absent for golf and did not do the activity. A lot of my struggle came from figuring out the equation for the points. To overcome the struggle I took the equation I already had and made adjustments to create the graph I wanted. From the first graph to the second the main thing I had to add was another point which I called point B. My setup on my first two gifs helped me with my third because i just added Sin squared x to the equation.The analysis of secant lines helps us because it helps you find the slope of the graph. I think slopes and trigonometry help pull the ideas together because they ith form the line.
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This week in AP Calc we have been exploring with limits some more. I thought I understood limits however I did not do very well on the quiz this week. I found the quiz challenging because I struggled with the trigonometry questions involving limits. I knew how to do the problems involving sin when it was an addition problem on the top of the function however I struggled when it was multiplication. I thought the homework was way easier then the test material. The sandwich theorem problems on the quiz really threw me off. I was not even sure how to begin to solve the sandwich theorem problem. I also struggled to understand salt and pepper functions at first. I think working together in our tables groups helped me understand the salt and pepper functions the most. One thing I understood really well this week was the laws of continuity three prong test. The three prong test of continuity is if F(c) is defined the function is continuous. If the limit as X approaches (c) exists then it is continuous and if the limits of F(x) = F(c). The main way I think about it is if the right and left hand limits do not match then it is not continuous. Overall I think this week was somewhat of a struggle but hopefully I will gain a better understanding of the new limit stuff with more practice.
We all have limitations in life and even in math limits exist. In AP Calc this week we focused on section one of limits. Most of the limits material covered this week was pretty easy for me because we did it in the third tri of pre calc. I was gone the day we did the limits lesson however, still managed to complete the homework with little to no struggle. The only part of the homework that took me a minute to remember was the right and left hand limits. However, when I did the homework I did not know that we hadn't gone over that part of the notes in class yet due to my absence on Thursday. The only thing that I did not understand at first was the the sandwich theorem. The sandwich theorem is where you are given a function usually including a Sin function and you use the function around the sin function to figure out where the sin function has a limit where it is being asked. Most of my learning this week came from looking at examples in the book and collaborating with others. I feel like limits are important for us to learn because I have heard that they come up a lot in calculus. I think that the first section of calculus is going to be a stepping stone for more complicated limit problems.
So far AP Calc has been extremely difficult. We are currently working on a review packet that covers the stuff that we learned in Pre Calc. The packet has been very hard because it is hard to remeber how do everything after a three month break. One thing that I had to work really hard to figure out was the decomposing functions. I struggled to remember which function went into the other function. The other thing I found really difficult was finding equations using equations from trig. This problem was extremely hard because at first I could not remember where to start. Once I figured out where to start it was hard to solve the equation due to my lack of memory about the unit circle. One of the things I did understand in the packet was solving for x. For the most part I was able to remember all steps that are involved with solving equations. I also had success when solving story problems. I think understanding story problems is important because it helps you apply mathematics in the real word. The problem I thought was really applicable to life was a problem that talked about how the change in emissions will increase the cost the of the scrubber. I found this problem, easy to understand because it was plugging in what you do not know to solve for what you do know. I'm the next few days I hope to regain knowledge in what we have previously learned but overall I think I will survive this class. Image citation: http://jasonstark.com/wordpress/2011/10/04/trigonometry-the-unit-circle/
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