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Material Type: Exam; Professor: Bernard; Class: Calculus II; Subject: Mathematics; University: Midwestern State University; Term: Spring 2009;
Typology: Exams
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Math 1734 Calculus II April 21 2OOg Test No.
(pleaseprint) Prof. Guy Bernard
There are six problemsfor a total of 100^ points. Calculatorsare allowedduring this test, but you must showyour calculationsin all problems.No books or notesare allowedduring this test.
c (,^ : 6,. =.^
'"e) (^) * (^1) ) = t - g 4 z
S = 1
( ' - (^) d x : 1 , , * + ( ; ' t ' J > "
) " u - ) > , I^! ,",-rf \
+/q l* J
"/rt 5 )t* (^) i+
T/'*" f
: 3 P - 1 o
Q*. .l
: r = ( i o ^ - :^ i I ^ J. d
B) Evaluate
.T.
No.2 (15 points)^ Doesthe following seriesconvergeor diverge? Justify your answer.Use any test you like. 6 ^ o
W " ' t
Ffr 7 ,*L^ ^\€.1^ (r- s"'t"-
(r-^ a) (*+ r)
1l'c'r1*, b
ha" Dr'rc,ecrci,uar*/eriotr TFsr
&
I ryre I
7- atw
No.3 (continued)
<I t -
-^ |^ -
| -
'Tl - 4
? t P (^) "r\
7 e (^) + Y b f u )^ \ + 7-
{ e^ :-rr t^ (2r.,-e^ ,o^.e-)
7G -+^ 7 7u., e+*:^ O^ -+
,tr.;- S :-^
r - (^4)
C
f n ' , T-: I '[ lt''*^ dr^ :-
c * Q &
a p*,._.,(+r)_r
_. :^ - g (^) I t L - Y " (^) : + C Y
7-
pa,ge
f 5 n 2 - L T r + 1 8 ,
f * - l 1 v a^ l (^ F ( " - , ) ( ' " 2 - ) L
A. (^) - r 1 7 -^ + (^) +. - y - t (^) Y - - r z (^) C >. - z - ) -
A (*-,)'^ +^ rs(u-,nk4^ <^ c &-l
Q<)Q.-o)"
6_Fzt1a 1tt^ -^ *^ rF-ljl+^
e(x-r) (v--)^ -t.^ e 6<<J
< d y = ' 1 2 -^ = D^ C : '^ +
9 t >. - = -^ I : , A o^
b
$r^..-
5 >? - n * + L 8^ :^ 6 ( 7 - ' z l - +^ B & - 4 ( v - v 1^
It *-.^ b ('t)^ + z-9 -^ Ll
6 * - l
r / , \ l L f - r. t - 1 1 v l l T^ b^ ( - l I^ r^ T
t * - , ) ( x * ) Y - t Y - L^ t t t - t J
1b,,-
No.5 (20 points)^ Doesthe seriesgiven^ below convergeor diverge? Justify your a,nsryer. Hint: Use the integral test. --r (^1)
u^ (^) n(lnn)
{u
{
, )
,,l.)r.f ,<,Arr.
aO
14*,
I hrTECrRAe (^) TFfT.
rN I l = ,^ J v
3 - Y
J.- -. I Jrz x
(* "=-X I ^ =_
tq^.N
t^"
,yJW
l$+
Th^^-
Ir^*"-,
tJ"^ ^l^ \x:.
1*--
Q-,.-
{.r
(w
At.^ h^^ "[l^
a,-^ ?nr,Y , ]r o
'r= f^ I^ J - * - - I *vtr L
' I^ ' o * - L t ' * )
&.x)"
f /q-^ r;scFe'tsiF'q^ ab^ E;".t)
-Tt".-
:f :- l* f .= J,.^, [ * -
. {
J : - 0 * \ * - t^ l " ^ u^ t N_+d t
--r.
[^. f
r -=*fr l , e (^) ) - - r ( - r \ t
t
J*.r -t-' f
T :^ 1,".- ) J^ ' J^ t u-** (^1) Tu !,,w;J f
l r - * -
DA
-T :^ f*-
d>..:-^ _L -r- :
J
vl-,"> !'-z-
?- (^) a-*j@QFlfi
ll'o^^-*
11*#,
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