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Calculus II - Test Four: Limits, Series, Convergence, and Geometry, Exams of Calculus

This 50-minute exam for math 252 calculus ii covers topics on determining the convergence or divergence of sequences and series, finding limits, calculating arc-length, and identifying the vertex, focus, and directrix of a parabola. Students are required to show their work and indicate answers clearly.

Typology: Exams

Pre 2010

Uploaded on 08/18/2009

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Math 252 Test Four
Calculus II name
This tantalizing fifty minute test covers several sections of Calculus by James Stewart 4th
ed. Clearly indicate your answers and show your work. All parts of problems are five
points each (unless otherwise stated).
1. Determine if the following sequences are convergent or divergent. If convergent, then
find their limit.
a) 3
3(1)
n
n

+−




b)
3
!
n
n
an
=
2. Determine if the following series are convergent or divergent. Give a reason for your
answer.
a) 2
1
cos(1/ )
n
n
=
b) 1.2
1
3
nn
=
c) 2
1
11
cos
nn
n
=



3. For which values of x does the series
1
2
3
n
n
x
=



converge?.
pf3

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Math 252 Test Four Calculus II name

This tantalizing fifty minute test covers several sections of Calculus by James Stewart 4 th

ed. Clearly indicate your answers and show your work. All parts of problems are five

points each (unless otherwise stated).

  1. Determine if the following sequences are convergent or divergent. If convergent, then find their limit.

a) 3 ( 1) 3

n

n

 (^) + −     

b)

3 n! a n n

=

  1. Determine if the following series are convergent or divergent. Give a reason for your answer.

a) 2 1

cos(1/ ) n

n

=

b) (^) 1. 1

3 n n

=

c) (^2) 1

(^1) cos 1 n n n

=

   

  1. For which values of x does the series 1

2 3

n

n

x

=

 − 

∑ ^  converge?.

  1. Determine if the following series are convergent or divergent. If convergent, then find their sum.

a) 0

5 4 9

n n n n

=

b) 1

ln n^1

n n

= +

c)

2 2 1

1 n (^ 1)

n n

=

d) 1

3 n

=

  1. Consider the parabola ( x +3)^2 = 4( y −5). Find the following. (3 points each)

a) vertex

b) focus

c) directrix