Download Final Exam 2 with Solution - Calculus II | MATH 1734 and more Exams Calculus in PDF only on Docsity!
; ' -? +
Math 1734 Calculus II April 21 2OOg Test No.
NAME:9":lI:!
(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.
No.1 (15points)
A) Evalutatethe sumof the^ series S :^ i t (l)"-'
c (,^ : 6,. =.^
'"e) (^) * (^1) ) = t - g 4 z
S = 1
the improperintegral ,^ :^
Io'
I
( ' - (^) d x : 1 , , * + ( ; ' t ' J > "
l x , : i J o * l
J,
^ ,L-v
J*
( + t r
l r l
) " 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.
-^ l^ -
No.2 (15 points)^ Doesthe following seriesconvergeor diverge? Justify your answer.Use any test you like. 6 ^ o
F 3r'
4 n = l h B\ + 2 ) ( n + 5 )'^ / \ '^ t
W " ' t
Ffr 7 ,*L^ ^\€.1^ (r- s"'t"-
(r-^ a) (*+ r)
t"
n?7|
1l'c'r1*, b
ha" Dr'rc,ecrci,uar*/eriotr TFsr
&
I ryre I
ilr- coF'\€Kq6^ D
7- atw
@'nl$+r'|
No.3 (continued)
<I t -
-^ |^ -
| -
'Tl - 4
? t P (^) "r\
7 e (^) + Y b f u )^ \ + 7-
t e + 4 t ; b n )^ <^ C -
{ e^ :-rr t^ (2r.,-e^ ,o^.e-)
7G -+^ 7 7u., e+*:^ O^ -+
,tr.;- S :-^
'/
r - (^4)
C
f n ' , T-: I '[ lt''*^ dr^ :-
I
I
O =-^ /Y,W^'
c * Q &
e)
Y .a'a- (4)^ +
a p*,._.,(+r)_r
_. :^ - g (^) I t L - Y " (^) : + C Y
x^ + c
7-
pa,ge
No'4(20points)
h9.J* l:ilffiTy"li'lJ;r"ionscarerury.
f 5 n 2 - L T r + 1 8 ,
r :
J 1r:t11*:ry4'
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
$r^..-
5 >? - n * + L 8^ :^ 6 ( 7 - ' z l - +^ B & - 4 ( v - v 1^
f - o
It *-.^ b ('t)^ + z-9 -^ Ll
- z - (^) * z - B
- L (^) = - (^) z - 9
6 * - l
r / , \ l L f - r. t - 1 1 v l l T^ b^ ( - l I^ r^ T
t * - , ) ( x * ) Y - t Y - L^ t t t - t J
1b,,-
No.5 (20 points)^ Doesthe seriesgiven^ below convergeor diverge? Justify your a,nsryer. Hint: Use the integral test. --r (^1)
u^ (^) n(lnn)
{u
{
, )
u)
r\
,,l.)r.f ,<,Arr.
aO
14*,
I hrTECrRAe (^) TFfT.
rN I l = ,^ J v
l.^ : -L
3 - Y
J.- -. I Jrz x
(* "=-X I ^ =_
tq^.N
t^"
A
,yJW
l$+
Th^^-
Ir^*"-,
tJ"^ ^l^ \x:.
1*--
Q-,.-
{.r
(w
At.^ h^^ "[l^
a,-^ ?nr,Y , ]r o
'r= f^ I^ J - * - - I *vtr L
E;}; ,^:^ )'*Y'
' I^ ' o * - L t ' * )
&.x)"
- (^) /.i- Latlsnii.'oitf r^ F-) -f (^) /\a-- Fa s tTivE- (^) * L.,.t)
f /q-^ r;scFe'tsiF'q^ ab^ E;".t)
No.5 (continued,
L U
-Tt".-
:f :- l* f .= J,.^, [ * -
\t-> ea^ I
. {
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*#,
<
- <-1t / - n z ' .r. 14^ ^--rt
n C-ePv€fa^ "F^5 cvUAA--
