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Final Exam 2 with Solution - Calculus II | MATH 1734, Exams of Calculus

Material Type: Exam; Professor: Bernard; Class: Calculus II; Subject: Mathematics; University: Midwestern State University; Term: Spring 2009;

Typology: Exams

Pre 2010

Uploaded on 08/16/2009

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;'- ?+
Math 1734 Calculus II
April 21 2OOg
Test No.2
NAME:
9":lI:!
(please
print)
Prof. Guy Bernard
There are
six problems
for a total of 100
points.
Calculators
are allowed
during this test, but you must show
your calculations
in all
problems.
No books or notes are allowed
during this test.
No.1 (15 points)
A) Evalutate the
sum of the
series
S : i t (l)"-'
c (, : 6,. =. '"e) * 1
)= t-g 4z
S=1
the improper
integral , : Io'
*.*
I
('- dx: 1,,*+ (;'t'J>"
lx,:iJo*l
J, ^ ,L-v J*
" ( +tr
lr l
)"u-
)>, I !
,",-rf \ +/q l* J
"/rt 5
)t* i+ T/'*"
f : 3
P-1o \
Q*.9 .l
:r=
(io^-: i
I^
J.
d
B) Evaluate
.T.
l-
-
-t-
-
-r-
pf3
pf4
pf5
pf8
pf9

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Download Final Exam 2 with Solution - Calculus II | MATH 1734 and more Exams Calculus in PDF only on Docsity!

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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^ -

  • t^ -
  • r -

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

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

  • I Y W > c O l J 1L

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--