Blog instead of Comments

So, since we really didn't do blogs over the holidays there isn't anything to comment on...so I will just review in a blog.

Taylor: they will give you c
f(c) + f^first deriv(c)(x) + f^second deriv(c)/2! (x-c)^2 + f^third dirv(c)/3! (x-c)^3

Maclauirn: is centered at 0
f(0) + f^first deriv(0)(x) + f^second deriv(0)/2! (x^2) + f^third dirv(0)/3! (x^3)

EXAMPLE:
Maclaurin up to the third degree

f=e^x
f(0)=e^0 = 1
f^1(0)= e^x(1) = 1
f^11(0) = e^x(1)(1) = 1

1+x+1/2! x^2
1+x+1/2(x^2)


Now don't forget about sequences and series! my fav :)
HERE ARE JUST A FEW THINGS TO REMEMBER ABOUT THE RULES:

p-series
1/n^p
p >1 CONVERGES
p <1 or =1 DIVERGES

geometric
(5/4)^n
n <1 CONVERGES
n >1 DIVERGES

limit comparison and direct comparison
*you must compare it to something easier
*use a different test
*then use this test to confirm first one

root and ratio
<1 CONVERGES
>1 or infinity DIVERGES
=1 INCONCLUSIVE

alternating series
*must take out the (-1)^n thing
*take limit MUST =0 or CANNOT be used


and something else we covered---

radius and interval of convergence:
*use the ratio test
*take the limit
*set up -1< x >1
*may have to solve