This week in AP Calculus, we started to take a look at calculating the area under a curve. By using geometric shapes such as rectangles, we can estimate the area of different things. For math, we are trying to calculate the area under the curve of a function. Using rectangles to calculate the area is not very accurate, so I am sure we will transition into finding a more accurate calculation for the area under the curve. So far, this section only uses basic math skills learned in geometry class. I am understanding this concept very easily. I have not struggled with anything so far, however the chapter just started. To calculate the area under the curve, you draw rectangles with LRAM, MRAM, or RRAM. These are where you have the rectangle intersect the function. You must multiply the height by the interval on the x-axis of the rectangles that you draw. You can calculate the area by adding the areas of the rectangles together. I thought that my participation in class was stellar this week. We are still just beginning to learn about the area under the curve, so I do not really have anything that I need to work on yet.
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This week in AP Calculus, we finished up chapter four. We learned more about related rates and differentials and had a quiz over it. We did some more review and had a chapter review assignment. It is important that we went over this stuff because we have a test over chapter four next week. All of this relates to previous topics because chapter tests are over the entire chapter plus previous chapters. I assume this will be leading us into chapter 5. I can only guess what is in chapter 5. I think I understood optimization pretty well. I didn't like related rates as much, but I got most of it. I struggled with a question on the related rates quiz. It confused me a little bit, but I understand how to do it now. To figure out a related rates problem, you have to set up equations that involve what you know from the problem. You take the derivative of the equation and plug in anything that you can. Since you took the derivative, you can now solve for any missing rates. My participation was really great this week. I still need to prepare for the test next week. http://www.textbooknbeyond.com/index.php?main_page=product_info&products_id=21542
This week in AP Calc, we applied what we know about derivatives to solve story problems. We found the derivative after setting up some equations to solve the problem. By doing this, we are able to optimize the problem in whatever way it wants us to. The derivative gives us critical points. Through this, we can determine the minimum and maximum of the problem. By using this method, we can do things like maximize the volume of a box. What you must do is set up the equations for volume of a box. Set up the variables you know. Find the derivative. Solve for the unknown variable. Plug this back into the equations if needed. The quiz over this went fairly well for me, but I think derivative applications was a fairly difficult chapter. We are now looking at rate problems. In these, we must understand the problem and how far and at what rate things are traveling. We must then differentiate the function with relation to time. Plugging in what you know will give you what you need to know. This is basically just a different type of application problem. We'll see how it goes, but I feel pretty decent about it. |
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February 2015
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