MATH 3001 W21
FINAL EXAM
:
4) Find all a >o such that the following tones converges :
C-opt]
z
lnfn
”
)
NII qh
4) Suppose that the series Ian converges conditionally and
h? I
A-opt] set pn= ; ( lannan ) . Show that Inpn diverges .
(3) For a>o, decide if the following genes is absolutely convergent,
convergent or divergent :
G-opt]
n
C- yh
( lnnjlhh
ya
–
(4) Let fnlxj = n fn
It’m
‘
hx ,
✗>0
.
Ppt] (a) Find the pointwise limit function f-1×1 .
Apt] f) Does fn converge to f uniformly on lo , a) ?
(5) Consider 1–1×1=2%1×1
4-pt) (a) Find all ✗ER so that the series converges .
[b-pt) (b) Show that FIN is continuous for ✗ c- C-1,1 ) .
(6) Use the Dirichlet test to show that Fogh
é
”
✓ht✗T
Copt converges uniformly on [90) .
(7) Find the Taylor series of f-1×1=
h×
✗
I
✗ 20
,
about
the point c-1 .
[“Pt)
what is the radius of convergence ?
Hotel : 70 points)
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