I am going into 11th grade this year and I am planning to take AP Calc AB this year. I am studying in the summer and I started limits this week and I am kind of stuck. I understand the basic rules and how to evaluate limits when x approaches a regular number. I get confused when x approaches infinity or zero and when the limit is of a sin, cosine or tan function. My main problem is basically remembering all the rules.
I have been searching for youtube videos, or websites that list out all the rules for evaluating limits for a really long time now, and I can’t find anything.
Can anyone help list out the rules or atleast give me a link to a website that could help me understand every type of limit questions and how to solve them. Thanks
At the Calc AB level there aren’t that many “rules” you need to remember (I think L’Hopital’s rule isn’t covered until BC, if I remember correctly).
Limits at infinity can be a bit tricky and you’ll just have to know which functions grow faster than others. For example, the limit as x → infinity of x^{10000}/e^x is zero, since the exponential function grows faster (alternatively, use L’Hopital’s rule).
Other times, you might be asked to compute the limit as x → infinity of P(x)/Q(x) where P and Q are polynomials. In that case, it depends on the degrees of P and Q.
Wait, there are tons of resources out there on the internet. You should be able to find at least some resources.
@MITer94 AP curriculum for Calc AB is changing next year(or this next I’m not 100%sure) but L’ Hopital’s rule is covered in AB now.
@MITer94 Thanks.
I have searched the internet for a concise method of solving through different limit problems. Problem is, every video i see is all over the place, and do not give a clean cut method of solving limits. Same with articles and websites.
@juvariashahid are you sure? I have seen lots of decent (but probably not very good) calculus tutorials on the web.
If you are expecting a clean-cut explanation, the best-written solutions, in my opinion, are usually meaningless unless you spend time futzing around with the problem at hand and trying different approaches, before looking at them.
I just started out on limits and I started studying directly from a AP CALC AB review book (I never took Pre-calc), so the concept of limits hit me hard and was very confusing. Thats why I think I wanted clean-cut explanations.
But, I finally found what I wanted at sparknotes…they give good explanations on how to do each type of problem and they used the limit rules to manipulate complex problems.
For anyone who ever comes across this and is struggling with limits, check out sparknotes limit explanation:
http://www.sparknotes.com/math/calcab/functionslimitscontinuity/section2.rhtml