Math 113 (Calculus Ii) Test 4 Form A With Answer Key - Brigham Young University

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Math 113 (Calculus II)
Test 4 Form A KEY
Multiple Choice. Fill in the answer to each problem on your scantron. Make sure your
name, section and instructor is on your scantron.
3
1. A power series for the function
is given by:
3
x
n
n
n
x
x
x
n
n
a)
b)
( 1)
c)
( 1)
n
n
n
3
3
3
n=0
n=0
n=1
n
n
n
d)
3
x
e) 3
x
f) none of the above
n=0
n=0
1 + x
2. Find a power series representation for f (x) = ln
.
1
x
3
5
2
4
3
5
2x
2x
2x
2x
2x
2x
+ · · ·
+ · · ·
+ · · ·
a) 2 + 2x +
+
b) 2 +
+
c) 2x +
+
3
5
4
4
3
5
2
3
2
3
x
x
x
x
· · ·
+ · · ·
d) x
+
e) x +
+
f) none of the above.
2
3
2
3
t
2t
3. Consider the parametric curve given by x = e
1, y = e
. Eliminate the parameter to find
a Cartesian equation of the curve.
2
2
2
a) y = x
b) y = x
+ 2x
c) y = x
2x
2
2
d) y = x
+ 2x + 1
e) y = x
2x + 1
f) None of the above.
4. Find a power series representation of the function
5
f (x) =
16 + x
2
and determine its interval of convergence.
a)
b)
c)
2n
5
x
5
n
2n
n
2n
|x| < 1
|x| < 4
5
( 1)
x
( 1)
x
x < 1
2n
16
4
16
n=0
n=0
n=0
d)
e)
f)
n
2n
2n
n
2n
5
( 1)
x
5
x
5
( 1)
x
|x| < 4
x < 2
|x| < 2
2n
2n
2n
16
4
16
4
16
4
n=0
n=0
n=0
g) None of the above.

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