This week we learned about continuity. We also talked more about limits. Talking more about limits cemented it more in my mind. I do not really like talking about continuity when it comes to piecewise functions. Piecewise function annoy me in general and then looking at them closer is just even more annoying. The 3 steps that we use to figure out if something is continuous are actually fairly easy. I like having rules telling me what to do for something like this. It makes me hate math a little bit less. I am still having trouble with being able to look at a graph and being able to tell whether or not it is continuous. Like I feel like piecewise functions should not be continuous but they are. At least I think they are. Are they? Anyway they just confuse me. Also the thing with the graph with vertical asymptotes. Is that continuous? I thought it wasn’t but I think in class we said that it was because the asymptote wasn’t in the domain. So is that it then? Like if there is something that has an asymptote at x=0 so zero isn’t in the domain, it would still be continuous. But it wouldn’t be continuous on the interval [-1,1] because then zero would be in that set of numbers. I guess that makes sense. Okay then I think I’m pretty okay with this now.
I have made it through my second week of calc and I have not died yet so things are looking pretty good. This week we learned about limits. Limits are the values that a function approaches as x approaches some number. There are different ways to find the limit of a function. The easiest way to find a limit (and my personal favorite because I am a lazy bum) is to use direct substitution. To do that I would just substitute the number that x is approaching for x. So basically if the thing is lim x->2 x2 -3x/x+3 then I would do 22-3*2/2+3 to get -⅖. So that means that lim x->2=-⅖. (I would have figured out the fancy way to write all of that out but it is 10:30 and I am tired so let’s just pretend that I did) Another way to find the limit of something would be to graph it. So I love my calculator and all but I really like Desmos for this. All I have to do is type in my function and then add a slider. Then it tells me the y values for whatever x values I put in using the slider. It is actually pretty nifty. I didn’t really understand this too well when we first started talking about it but now I get it. The video really helped so that was good. Now I understand how to do this so yay! Math!
I did not really learn anything new in math this week. It was all just review from last year so it was pretty easy. The only thing that I did not remember was the formula for volume of a sphere and the formula for the area circle. I just googled those and then used them, so that was kind of boring but it was the most interesting thing I did in math this week.The two triangle problems were annoying because I forgot trig stuff but then Kathryn helped me. Now I remember how to do it and that is petty cool. The review helped me when I retook the ACT on Saturday. There was a lot of stuff on the ACT that I did not remember until after I did the review sheet. These thing will help us when we actually start to learn new things. I do not know this for sure but I am going to assume that what we are going to learn things that relate to what we reviewed. Otherwise reviewing it would not make very much sense. I still need to work on remembering formulas for volume and area because I just googled them and I already forgot them. Oops... Maybe if I put a picture here I will remember but I do not really know...
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