AP Calc BC test...


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AP Calc BC test...



I am cramming some additional information just before the AP Calc BC exam.
I need help with the following 6 problems (detailed directions on solving
them...NO HINTS PLEASE, just detailed solutions):

1)  In decomposing (8x - 7) / [(x - 2)(x + 1)], by the method of partial
fractions, one of the fractions obtained is

A) 2 / (x - 2)
B) 3 / (x - 2)
C) 4 / (x - 2)
D) 9 / (x - 2)
E) 27 / (x - 2)


2)  The graph in the xy-plane represented by x = sec t and y = tan t, for
-[pi]/2 < t < [pi]/2, is what shape?

3)  The third-degree Taylor polynomial about x = 0 of ln (1-x) is:

4)  What is lim(x -> 0) [(tan x - sin x) / x]?
(This one I think I messed up somewhere in the math...possibly the
derivative of (sec x)^2 = 2(sec x)^2 * tan x, I think that's right, but I'm
not sure)

5)  Let g be the 7th-degree Taylor polynomial for sin x centered at x = 0.
(How do I determine when a Taylor polynomial is greater or less than the
object it is conforming to?)  Which of the following is true?
Answer:  g(x) > sin x for x < 0, and g(x) < sin x for x > 0.

6)  The area of one loop of the graph of the polar equation r =
2sin(3[theta]) is?

BTW, what is Euler's method?  I probably know how to do it, but under
another name (or just the formula without the author...I just love all the
plagarism in my calculus book that I own :)

Thanks for any help.


        Thomas J. Hruska -- shinelight@detroit.crosswinds.net
Shining Light Productions -- "Meeting the needs of fellow programmers"
                   http://www.shininglightpro.com/

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