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Unformatted text preview: MATH 1005F Test 4 November 23, 2009 1 ;. This test paper has yfquestions and total of 30 marks. It cannot be taken from the examina—
tion room. Only nonprogrammable calculators are allowed. Duration: 50 Minutes. NAME : STUDENT NO : PART I: Multiple Choice Questions. No partial marks. Circle the correct answer. (—1)” 5” n?
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n3 [3] 1. What is the radius of convergence of the power series 2 nzl <a>o .§ (as (d); <e>oo 5n+1 n3 .«: SQJ—waas‘ W4”) {:1 ﬂ ‘+ i / g I’? n’f‘i
‘ o, n C“ 1‘
I
K —— "E
00 n2
[3] 2. What is the radius of convergence of the power series 2 11:" 7
2" n! 1 :1
(b) 5 (c) 2 (d) 1 (e) 0 '2, 00+} MIL, ‘, 3:21.. .. .ﬁlﬂﬁl‘kw)
on 2” (Mi), 0
.. 0.0 [3] 3. You are given that the radius of convergence of the power series 2 W ' IS 1.
_ 37L + 1
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W hat is the interval Of convergence? (a)(*1,1) (1)) [2,4) (C) (3,5) .(3i5l (6) [3,5] iris/3 (70/1,, INA/.4 IFS
0“ n “ Z M 2’:
3., ZN ("1 , W are *
X1 .. 30,“ h?!
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X’ " 3n+l MATH 1005F Test 4 November 23, 2mg 2 PART II: Long answer questions. Show all your work. [3] 4. Find the radius of convergence and the interval of convergence of the power series farl)". n21 AN 1 A do @
ﬂ [XV—J n ; "fl/:7”, I); 0 K04 >/\ OW
v7 er » 5[5]. Find the radius of convergence and the interval of convergence of the power series
C13 2%(I—1Yl' r)
waﬁ—»%W MIL¢%U%
n ‘/ 3 ﬂ n i if om 4m [MATH 1005]? Test 4 November 23, 20097 3 [7] 6. Find the radius of convergence and the interval of convergence of the power series i<$n+7f)n' ﬂ
”:1 ﬂ 9") 2; 7+!)
J’— ) 9111)] : "1"”: ’ I
Om 1 h :L“ Q” (n+1) ?n I ’3 ,3+}:Q
../5?:»/0 n
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@359 X" ‘ n?” no MATH 1005F Test 4 November 23, 2009 4 7. Find a. power series representation for the following functions: [31(a) f(:v)= 3i méi'
\Y/e, Lnow M 3 2740) IX “‘59 ap/H , n 3H4
0p 1) 3n” _' X
X ZN) X ’ Z( )
35,, ” mo ...
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