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10 Questions on Divergence and Convergence Series - Final Exam | MATH 1220, Exams of Mathematics

Material Type: Exam; Professor: Ghoreishi; Class: SI Calculus II; Subject: Math; University: Weber State University; Term: Unknown 1989;

Typology: Exams

Pre 2010

Uploaded on 07/23/2009

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Calculus II
Sample Exam III - 4 pages
Sections 11.3-11.5 & 12.1-12.5
Math 1220
NAME:
TIME LIMIT 50 MINUTES
The point value of each problem is in the left-hand margin. You must show your work to receive full
credit for your answers.
(10)
1. True or False.
( ) (a) The sequence
a
n
= (
,
1)
n
converges.
( ) (b) The series
1
X
n
=1
tan
,
1
n
converges.
( ) (c)
1
X
n
=1
3(0
:
4)
n
,
1
= 5.
( ) (d) In polar co ordinates, ordered pairs (1
;
4
๎˜™=
3) and (1
;
,
2
๎˜™=
3) represent the same point
in the plane.
( ) (e) The graph of
(
x
,
1)
2
25
+
(
y
+4)
2
49
= 1 is an ellipse.
(6)
2. The sequence
n๎˜
n
n
+1
๎˜‘
n
o
1
n
=1
converges. Find its limit.
(6)
3. Show that the sequence
n
5
n
n
2
+1
o
1
n
=2
is bounded and monotone.
pf3
pf4

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Calculus I I Sample Exam I I I - 4 pages Sections 11.3-11.5 & 12.1-12. Math 1220

NAME:

TIME LIMIT 50 MINUTES

The p oint value of each problem is in the left-hand margin. You must show your work to receive full credit for your answers.

(10) 1. True or False.

( ) (a) The sequence an = (1)n^ converges.

( ) (b) The series

X^1

n=

tan ^1 n converges.

( ) (c)

X^1

n=

3(0:4)n^1 = 5.

( ) (d) In p olar co ordinates, ordered pairs (1; 4  =3) and (1; 2  =3) represent the same p oint

in the plane. ( ) (e) The graph of (x1)

2 25 +^

(y +4)^2 49 =^1 is^ an^ ellipse.

(6) 2. The sequence

n

n n+

n o 1

n=1 converges.^ Find^ its^ limit.

(6) 3. Show that the sequence

n

5 n n^2 +

o 1

n=2 is^ b^ ounded^ and^ monotone.

(18) 4. Determine convergence or divergence of the following series. State the tests used and show your work.

(a)

X^1

n=

n

ln n

(b)

X^1

n=

2 n^ n

2 n^ (n^2 )

c)

X^1

n=

(1)n

p 3 n 2 + 1

(10) 8. Covert from p olar co ordinates to rectangular co ordinates or vice-versa.

(a) P = (r;  ) = (6;  3 )

(b) Q = (x; y ) = ( 5 ; 10)

(10) 9. Find the equation of the tangent line to the graph of the p olar curve r = 2 + cos  at  =  = 2.

(10) 10. Find the area of the region in the plane enclosed by the cardioid r = 2 2 sin .