I'm starting to feel as though my final grade in this class will definitely not what I want it to be. This past week I took the Chapter two test and I only got a 75 percent. But we've started a new chapter and I feel as though it will be a fresh start as we continue on with this chapter. Also this week I learned about the ability to get test points back by completing "Demonstration of Mastery" assessment. I feel quite confident with the new derivative topic. When the class went into the lab I picked up the central ideas pretty quickly, hopefully that will still be true on the upcoming 3.1-3.2 quiz! With the derivative topic, I feel as though it is a more clear and straightforward concept, where as I found limits and continuity to be somewhat difficult due to the large amount of possible functions that needed to be simplified.
When the class went to the lab we started to see that the derivative has a few special connections with its function; one example includes how the maximums and minimums of the function are the zeros of the derivative of that function. Now the main idea and point of the derivative is to show the slope of the tangent at any point on the curve. This can be seen on many "Curvey-Curves" but does not work on a "curve" consisting of only line segments, therefore the derivative can not be calculated on a corner because corners have infinitely many tangents. With respect to this week I plan on next week being a lot less stressful (knock on wood). Continuing with the derivative and everything associated with it should be one of the more interesting things that I look forward to. -Have a great weekend Mr. Cresswell! (unless you don't see this before it's over!)
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Throughout this last week I've had quite a bit of catching up to do. I haven't had the best luck with the concept of limits ( which can be seen on my last assessment grade :( ). This is probably due to my lack of classroom time while I was sick. No matter the excuse I'm trying to learn the concept more and more each day, hopefully leading up to a confident test day!
Moving to the later part of the week Deepa and I began trying to use Desmos as a model for what the tangent of a circle was. Although this did take a while (mostly due to the lack of knowledge on how to use a Macintosh with Snagit) everything began to come together. Deepa thought of a correct way to enter the functions needed to create the assigned graph, as well as the creative ones. This activity's entertainment was only catalysed by Deepa's attempt to pronounce "GIF", otherwise known as "GIFE" to her! I'm sure on any of the GIF files made that one can here Deepa struggling with this! :) With all that set aside we finally found that the graph's functions were centered around one single function, g(x)=(f(a)-2)/(a-2)*(x-2)+2. The set point being (2,2). So for the week many struggles as well as accomplishments can be seen. But with the use of group members and late night studying the struggles became fewer in number. Looking forward to another week of learning as well as teaching. But I'll end with this, Mr. Cresswell, how are you liking your new iPhone? Might want to check this video out about it! Discovering my own LimitsDuring the first full week of school we have both taken a test on pre-calculus topics and we have started to learn about limits. Limits are looking at what an equation approaches to without actually using the number asked to find the limit for. The variables in limits are often just one one-thousandth away from the desired number. What I have learned during the duration of our studies with limits is that being able to solve fractions and make it so zero is not in the denominator is very important to solve the limit algebraically. The limits may be used later to introduce the concept of continuity. What I understood the most was that my fraction solving skills were very good! I understood how to enter limits in my calculator and use the table feature to find the limit. Now this may be useful but I did kind of struggle with any limit equation that involved trigonometry. Limits with equations consisting of sine, cosine, and tangent are what specifically struggled with. Now I have been studying over this more in order to become better at them for when the test over them comes; I’m sure there will be a no calculator portion to the test over limits. My participation while learning and studying this week has been very apparent. I have interacted with others and collaborated about how to do specific problems or topics. With the help of classmates and my instructor I have become progressively better at limits. As stated above I still have to work on my ability to solve trigonometric limits, which I plan on doing over the weekend! So while I may not have a mastery over limits so far, my progress with learning them has increased and my goal over the weekend is to get a better understanding of limits that have trigonometry. Although I haven't started the addition, subtraction, multiplication, and division multiple limits, I have looked over how to do them and I feel confident i will have much success with that area of limits. In conclusion although limits have somewhat been challenging to me I believe that with a little more practice I will become proficient in the subject!
These last few days I haven't so much have learned calculus as much as I have brushed up on my pre-calculus skills. I have come to the realization that I have forgotten quite a bit over the summer and I think that this pre-requisite packet was a very good idea. I forgot ideas such as composition and decomposition of functions, logarithms, finding the volume and surface area of a sphere, and finding vertical asymptotes; although this pre-requisite packet has made all of these ideas come freshly to my mind. These topics are obviously leading into the calculus portion of this class, which is why they are important. this week I have understood how to reduce functions very well; I have also flourished in my ability to find the volumes of most shapes. Although I did struggle with some other topics as well; these include logarithms, volume and surface area of a sphere, as well as finding vertical asymptotes. Right away I found out how to find vertical asymptotes, although the logarithm portion took far longer to refresh my memory on. One particular problem that was especially difficult was solving a function for X. This problem was Ln(X)=2T+Ln(2). After numerous Google searches I eventually found the correct way to solve this problem through this site. The above picture is my method of solving the equation. The topic of solving logarithms is one that I particularly went in depth on. The canceling of natural log with e was the most difficult thing to relearn as well as subtracting natural logs then become Ln(x/y). Overall these last four days have helped immensely and I look forward to the future of this class and all the knowledge that will be learned |