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Unformatted text preview: Exam 321. Name: @\ Ml 75—001 (1 pt.)
Iran, 2009 1. (10 pts.) Consider the sequence _ n+3_ I
_2n—1’ '— an (a) Graph the ﬁrst; six terms of the sequence on the axes provided below. Be sure that your
axes are properly labeled. 3 H i i é (b) ComputeI1i111_e...n. (90 z I" ) at: l 3Q; ' 3 ) a; S
n—>.’x. ‘ 51. 6] 2. (25 pts.) Determine if each of the following is convergent or divergent. CIRCLE YOUR,
ANSWER. You do not need to Show work= but you earmot. receive partial credit for a wrong
answer unless I can see how you got your answer. / "xxx 00 n. — 1 _ .
a — DIVERGENT
( ) Z .a'nﬁ + 2.” n=2 a... INVERGENTE 00 n2 + 2111 n T .1 (m 2:75jiﬁf— CONVhRGle INVERGENT
m 2 4 /xrr’ff::r~\
I n + _ 'H. l _‘ 1
(d)§: T6” CONVERGhNT (:HinyReENfraem>
'n=0 —_._._____.H_._——r/ ,F _ _ DIVERGENT . T
(a 2:35 CONVERGENT 2. (25 pts.) Determine if each of the following is convergent or divergent. CIRCLE YOUR
ANSWER. You do not need 1.0 show work: but you cannot receive partial credit for a wrong
answer unless I can see how you got your answer. DIVERGENT w n2 —— 211110. 1 r 1
(b) 2 CONVERGle DIVERGENT
°° 271+ 4'” f’ __'_“_r_::\
(d) 2 Mn CONVERGENT DIVERGENT we
n.=0 " I (e) 4 CONVERGENT DIVERGENT n=0 3. (5 pts.) 011 the previous page there is exactly one geometric series. (a) Which one is it? ( CB (b) If it converges, compute the exact sum of the series. if it diverges, explain why. 5 2(2)“ H 4. (10 pts.) Find the radius of convergence of Z ILL—ii;
2ni1
n=2
2 ﬂ " I n t I
an ' T n ' “ ﬂ " 2 “.1 (3X1Z) Z
3x+2
_ \ ¢ < i
2
“2 < 3¥+ Z 5 Z
.. Li c EA (— 0
~ 11/3 c x( O
455/ O
r 3 . v __ _ a.
A 2.
(cam/Led: “2/3 J AJVOJ' 3 5. (10 pts.) Express ﬁx) 2 3 2 as a power series centered at U.
— :1: = i __z—— : Zi[l+ EX’“ (%“3'T<
3 1— Ex 3
III J '. Z L “i 3 S5 R
__ ———~ '~#— 1' __‘X “" WK +
* 3 x “L 61 A 2.7 SH {5. (10 p135.) Find the quadratic approximation for = (1 + 11:)U3 centered at U. M a ‘
M 1+ ( 1 Ex + (2.\)\
3: l _k_ + (3 xi
2: l J— }.m L_
I I —+' ,3 X _ a X I 7. (10 pts.) Find the ﬁfth order approximation of cenLOI‘ed at 0, given that = 2 and
the derivative of f is ,Hzcosa;
f0») 1+3?
JZIA. ’(m .. (/ﬂl 2 i a ({ 1+ 9
N {+Ki: ‘ 5x +2q)‘ X X.
Z
 l— A ’r 2H
t K
 1x2 + lax ~ ixé
_L ~+ I 6 l_ .9
+291)“ * 31X flax
/ 3 z '1
LK3 +1 37»;
1C 1: 6* x# Z {20 ...
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 Fall '08
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 Calculus

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