I don't know why but I feel I kind of like limits after all.. because I have to picture some of the problem in my head specially when the limit of x approaches to +- infinity and it makes me understand it better...
HOWEVER....
1.) sometimes when the problems involve sin(x) I get confused. This is because it takes me time to understand how sin(x) as it approaches infinity it's equals 0 .I remember that's the answer but correct me if I'm wrong. I know sin(x) it's always between 1 and -1 but it's not like f(x)= 1/x where the function gets very close to 0 as it goes to infinity...ITS WEIRD.
2.) I also have trouble determining the limits when we have to look at graphs and there is that one filled dot by itself either above or under other open dot that is part of a line. That messes my head up. :-S
3.) Other concept that eludes me it's when we have to find the Right end behavior model and Left end behavior model of a problem like this one y=x^2+e^-x.
First I graph both lines and then I try to figure out to which one each side it's gonna look like but it's really hard. I try not use the calculator but I have toooo...it's sad :(
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1) sin x does NOT approach zero actually. (sin x)/x approaches zero as x--> infinity. sin x usually just becomes insignificant compared to other numbers that grow really big because the extent of it ranges between 1 and -1.
ReplyDelete2) haha. That one dot doesn't matter when talking about limits. It doesn't matter what is happening AT that point c, just around that point c.
3)haha. your posts are so cute. It's not sad, you just have to memorize the graphs! =P For something like x^2 and e^x, you just have to memorize each of them separately, not added together..