Power Series is something relatively easy, and I found the homework for both this and thee Maclaurin/Taylor Polynomials to be extremely redundant. However, there's like only two basic rules for Power Series.
1.Do the ratio test.
2 set the limit of the absolut value less than 1
3. solve.
Basically this is just a review on the ratio test. HOWEVER. Say I have after the ratio test
limit as n-inf. of abs(x^2/2!)
Now this is the thing. the limit of the abs value is set to less than one right? well, if I plug in infinity, it'll give me inf over a number. which is just infinity. Therefore it diverges. HOWEVER,once again, if I plug in say 1 for x, I'll be left with 1/2 which is less than 1 but not greater than -1 (coming from the absolute value thing where you put -ve < inside of abs< +ve) value . if I plug in 0, I'll be left we something less than 1. therefore at both x=1 and 0, the polynomial converges (aka no infinity)
For what I do not get, and perhaps a question for Brob is exactly how this will be phrased on the AP. Also, I would like to know what to do with the graph ones?? Thanks oh so much.
Subscribe to:
Post Comments (Atom)
it will immediately state to use either type..it'll never ask you to pick this way of solving from the top of you head. :)
ReplyDeleteps..never forget which type is ALWAYS centered at ZERO!
ReplyDeleteI'm thinking that on the AP they will either be straight up about it like asking you the convergence of the power series or they may just say the convergence and you pick your own method. Not completely sure.
ReplyDeleteadding on to steph's comment, the type that is always centered at zero is maclaurin series!
ReplyDelete