This week we continued to learn how to rotate solids around an axis in a plane. The main focus was the shell method and so far it's my favorite method. To use the shell method you multiply the integral of the function's area times its height (usually x or y plus or minus however far it is from the x/y axis) by 2pi. With the other methods I was confused on how to rotate around an axis other than the x and y because you had to subtract the function from the numbers or vice versa. I feel quite confident with the shell method and the test shouldn't be too diffucult. Can't wait to learn more!
This week for AP calc we learned how to find the area of a region between two curves. First, we learned how to find the area by taking the integral in terms of x and then we learned how to do it in terms of y. We also learned about the connections between position, velocity, acceleration, and jerk. At first I didn't really understand what we were doing for section 7-1 (the velocity/position chapter) and I struggled with making the connection between the graph of the velocity function and the direction and stuff the object was moving. After asking Mr. Cresswell as well as my peers, I understood the concept. Finding the area between curves was actually really easy. You take the integral of the top function minus the bottom function in terms of x if possible, and if not, the you take the integral of therightmost function minus the left in terms of y. We had a quiz over sections 7-1 and 7-2 on Friday and I feel pretty confident on how I did. Overall, this chapter was pretty simple. Exams are next Thursday (ew) and after that we are basically finished. Can't wait to learn more! Khan academy help:e
This week for AP calc we learned more about u-substitution and spent a lot of time on slope fields. I am now pretty confident in my ability to integrate functions, so this chapter was really quite easy for me. The new thing that we learned this week was sloope fields. I haven't really figured out how learning about u-substitution led to slope fields, but I'm totally fine with it since it's so simple. Basically, slope fields are a drawing of all the possible functions that you can get from dy/dx. It symbolizes different functions with different values of "c". You draw slope fields by plugging in values of x and y into their respective spots in a differential equation, and the number you get is the slope at that certain point. For example, if dy/dx=x+y, then the slope you draw at the point (2,2) would be 4. After drawing the slope fields, you can then approximate the curve of a specific "c" value by stating what point on the y- axis you want the curve to go through. like (0,5). It's kind of hard to explain in words, so If it doesn't make sense, I've attached a Khan Academy video because they (obviously) do a way better job explaining than I do. We had a quiz on Thursday and I felt like I did pretty good. Chapter seven is the last chapter we need to cover for the AP test, and I can't wait to learn more. Slope Field of dy/dx=x+y:At this Point in AP Calc, I've kind of just accepted the fact that the rest of the course is going to be over derivatives, integrals, and how to apply them in different ways. How fun. Not that I'm complaining. After we finished the short answer portion of the chapter five test on Monday (which completely butchered me), we began chapter six. The rest of the week was spent re-learning u-substitution and learning new ways to apply it. I still remembered how to do basic u-substitution from the fall, so this wasn't that difficult. One concept that I struggled with was how to do u-sub in definite integrals. I sometimes forgot to insert the bounds from the original integral into u to get new bonds for the new integral. I also feel like the problems that we are doing now are a lot more difficult than the rudimentary ones we did in the fall. I asked my peers for help when I needed it, and checked my answers in the teacher's edition. Overall, chapter six has been relatively simple, and I really hope the rest of the chapter is like this. Can't wait to learn more!
For this week of AP calc we learned about one of the most fundamental concepts in calculus-- the fundamental theorem of calculus. I relied on learning the fundamental theorem of calc mainly through inductive reasoning. This does not surprise because I usually use inductive reasoning to solve problems/learn things. The proofs of the theorem confused me and I understood how to apply it better through the examples.Through the examples, I understood the proofs and equations. I understand how important the theorem is because it is literally the bulk of calculus. In order to do higher order calculus, it’s important to understand the theorem. It draws the connection between integrals and differentials by saying that the derivative of an integral is equal to f(x). I think it’s kind of redundant because I figured out the connection way before we learned about the theorem, but I guess this just explicitly states the relationship and makes it legit. Fundamental Theorem of Calculus:
Khan Academy help: https://www.youtube.com/watch?v=Ef22yTJDUZI
Week Eleven/Week One: A New Beginning/Applying Derivatives (FOR THE SIXTH WEEK IN A ROW??????)12/6/2015 Chapter Four got me like:This week for AP calc, guess what we're still learning about? DERIVATIVES!!!!!!!!!!!!! WHAT A SURPRISE!!!!!!!!! I'm going to assume that the rest of calc is going to be expanding upon derivatives because THAT"S WHAT IT IS RIGHT NOW! So, on Monday we continued to review for the section 4.1-4.3 quiz that we took on Wednesday, and basically the entirety of the first three sections was about how to find maxes, and mins from the first derivative, and how to find inflection points and concavity with the second derivative. I felt like after reviewing I understood how to do these things a lot better. Before reviewing, I was really confused on how to find critical points to find the maxes and mins. I did not realize that the end points of a closed graph were considered critical points. i know that it was in the notes, but I guess that it just didn't hit me... i ended up getting a 21/24 on the calculator portion of the quiz, and a 15/15 on the no calculator portion of the quiz. i did better than I thought I was going to, to be completely honest. On Friday we started learning about optimization, which SURPRISE!! IT USES DERIVATIVES!! I understood all of the notes and examples, so I thought that the section and assignment were going to be easy, but BOY WAS I WRONG. I started he assignment last night and I realized that I really don't know how to do a lot of it. Or, it took me 5 minutes to figure out a problem. I'm going to have to go back tomorrow and work with my peers (cough, Eric) to figure out these problems. Can't wait to learn more! (Just kidding, I can totally wait to learn more.)
This week for AP calc we FINALLY finished chapter three. FINALLY. Monday and Tuesday were spent reviewing for the chapter three test which consisted of concepts like the chain rule, u substitution, antiderivatives, power rule, trig rules etc. etc. etc. The test was on Wednesday, and I felt pretty confident about. Honestly though, even if I failed it (which I doubt) I could just do a mastery. For Thursday we did an activity for section 3.4 where we got into groups, analyzed distance/time graphs and acted them out. It was really fun and it helped me analyze graphs better. On Friday, Cresswell wasn't here and we were supposed to begin chapter four. Instead, we did another section 3.4 worksheet. I did not really understand the worksheet that well, but I got help from my classmates that I was working with. What I got out of that worksheet was that in a graph of position and time, the derivative of that graph would be acceleration, and the absolute value of the acceleration would be speed?? The exam is in about a week and a half and I feel pretty confident about it. I think that the spired tests really helped me lowkey review without me putting in much effort. I'm wondering if we are still going to take a quiz over section 4.1-4.3 during this trimester because I don't exactly know how that's going to work. Thus concludes my final blog over derivatives. Good riddance. Can't wait to learn more!
why won't this end?This week for AP Calc, we're still learning about derivatives (I know, SHOCKER right?) We learned about implicit differentiation, how to take the derivative of trig functions and inverse trig functions, and also how to find the derivative of exponential, e and natural log functions. We took a quiz on Wednesday over the chain rule, u substitution and implicitly defined functions. I did pretty well and got a 22.5/23. I feel like I as we learn more and work more with derivatives, I am getting a better understanding of how derivatives work. T the beginning of chapter three, I was confused about the concept of derivatives, and when we learned rules such as the product rule and chain rule I got even more confused. However, after doing the same thing for about four weeks I'm fairly confident with what I am doing now. At this point it just feels like I'm learning new rules and it's not that big of a deal. The chapter three test is supposed to be next Wednesday which means that we'll FINALLY be done with derivatives. one concept that I struggled with this week was implicit differentiation. I did not really understand that d/dx of y was equal to dy/dx and that (d/dx)y^2 was equal to 2y(dy/dx) because you would treat y^2 as a chain rule function. I asked my peers for help while doing the homework assignment and they ended up helping me get it. Overall I thought that the things we learned this week were pretty easy, and I honestly can't wait to be done with derivatives. Can't wait to learn more
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Sarah ZhaoI like cats. Archives
March 2016
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