BC CALC 3
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Quiz #5
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#1(6 pts) Find the interval of convergence for the following power series. Show all steps
clearly. Check endpoints!


n 1
(1)n  3n ( x  2)n
n  4n
#2(9 pts) Find a power series with the given interval as its interval of convergence. No work
necessary, though partial credit may be given.
a. [1,1)
b. [3,1]
c. (4,10]

#3 (8 pts) Suppose that the power series
 a ( x  1)
n0
n
n
converges if x  3 and diverges if
x  8 . Indicate whether the following statements must be true, which may be true, and which
cannot be true. Justify your answers.
a. The power series converges if x = 2.
b. The power series converges if x  4
c. The power series diverges if x = 5.
d. The power series converges absolutely if x = 4.
#4 (6 pts) Suppose P2 ( x)  a  b( x  2)  c( x  2) 2 is the second degree Taylor polynomial
for f centered at x  2 . Determine the signs (positive, negative or zero) of a,b, and c if the
graph of f is shown below:
#5 (6 pts) The Maclaurin polynomial of degree 100 for some function f is given by
1 2 x 3x 2 4 x3 5 x 4 6 x5 7 x 6 8 x 7
101x100
P100 ( x)  







2! 3! 4!
5!
6!
7!
8!
9!
102!
a. Find f (0) .
b. Find f (60) (0) .
#6(8 pts) Find the Taylor polynomial of degree 3 for g(x) = x3/2 centered at 16. That is,
with x0 = 16 and n = 3).

1
. Note that this is not a
n( x  3) n
n 1
power series; the convergence set is the set of all x for which the series converges.
#7(2 pts) Find the convergence set for the series

#8(2 pts) Find all x which satisfy:
 2x
n 0

2n

 3 x 3n
n 0