Math 155 Section 02
Calculus II
Final—Take Home (Last Name: A–C)
Name: __________________,
___________________
ID: ____________
Last (print)
First (print)
(last 4 digits of SSN)
1.
Binomial Series
[12]
a) Expand (4
a
– ½
b
)
4
.
[3]
b)
Expand (2 +
x
)
2/3
as a power series. Include the term containing
x
3
before using the ellipsis (…).
[6]
c) Approximate 1.9
2/3
using quadratic
approximation. (Hint: use answer from part (b) and check your
answer with your calculator.)
[3]
2. Taylor Series
[10]
a)
Find the Taylor series for ln (2
x
+ 1) centered at
x
= 3. Include the term containing (
x
– 3)
3
before using
the ellipsis (…).
[8]
b)
If
1
2
2
)]
1
2
[ln(
+
=
+
x
x
dx
d
, find the Taylor series for
1
2
2
+
x
centered at
x
= 3. Include the term containing
(
x
– 3)
2
before using the ellipsis (…). (Hint: use answer from part (a).)
[2]
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Area Bounded by Two Polar Regions
[10]
a) Give the polar equations of the two congruent circles shown on the right,
Circle 1:
r
= ________
Circle 2:
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 Spring '11
 HaHe
 Math, Calculus, Power Series, Taylor Series, Cartesian Coordinate System, Binomial, Polar coordinate system, Conic section

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