High School
SAT
SAT Elite 1500
SAT Tutoring
ACT
ACT Elite 33
ACT Tutoring
University
MCAT
MCAT Elite 515
Med-School Admissions
Pre-Med Tutoring
Pre-Med Plus
LSAT
LSAT Elite 170
LSAT Self-Paced
LSAT Tutoring
DAT
DAT Elite
DAT Tutoring
Log in
Get Started for Free
Practice: Integrating a Power Series*
Related Topics
Wize University Calculus 2 Textbook > Power Series
Functions and Power Series
8 Activities
Practice: Power Series Representation
Find a power series represetnation of
f
(
x
)
=
x
arctan
x
2
f(x)=x\ \arctan x^2
f
(
x
)
=
x
arctan
x
2
and determine the radius of convergece.
Part 1
Part 2
The power series representation is
x
+
∑
n
=
0
∞
[
(
2
(
−
1
)
n
x
4
n
+
3
(
4
n
+
3
)
)
(
1
4
n
+
2
+
1
)
]
x+ {\displaystyle \sum_{n=0}^\infty} \left[ \left(2(-1)^n\frac{x^{4n+3}}{(4n+3)}\right) \left( \frac{1}{4n+2}+1 \right) \right]
x
+
n
=
0
∑
∞
[
(
2
(
−
1
)
n
(
4
n
+
3
)
x
4
n
+
3
)
(
4
n
+
2
1
+
1
)
]
x
+
∑
n
=
0
∞
[
(
2
(
−
1
)
n
x
4
n
+
3
(
4
n
+
3
)
)
]
x + {\displaystyle \sum_{n=0}^\infty} \left[ \left(2(-1)^n\frac{x^{4n+3}}{(4n+3)}\right) \right]
x
+
n
=
0
∑
∞
[
(
2
(
−
1
)
n
(
4
n
+
3
)
x
4
n
+
3
)
]
c
+
2
x
+
∑
n
=
0
∞
[
(
(
−
1
)
n
x
4
n
+
5
(
4
n
+
5
)
)
(
1
4
n
+
2
+
1
)
]
c+2x + {\displaystyle \sum_{n=0}^\infty} \left[ \left((-1)^n\frac{x^{4n+5}}{(4n+5)}\right) \left( \frac{1}{4n+2}+1 \right) \right]
c
+
2
x
+
n
=
0
∑
∞
[
(
(
−
1
)
n
(
4
n
+
5
)
x
4
n
+
5
)
(
4
n
+
2
1
+
1
)
]
D
+
C
x
+
∑
n
=
0
∞
[
(
2
(
−
1
)
n
x
4
n
+
3
(
4
n
+
3
)
)
]
D+Cx + {\displaystyle \sum_{n=0}^\infty} \left[ \left(2(-1)^n\frac{x^{4n+3}}{(4n+3)}\right) \right]
D
+
C
x
+
n
=
0
∑
∞
[
(
2
(
−
1
)
n
(
4
n
+
3
)
x
4
n
+
3
)
]
D
+
C
x
+
∑
n
=
0
∞
[
(
2
(
−
1
)
n
x
4
n
+
3
(
4
n
+
3
)
)
(
1
4
n
+
2
+
1
)
]
D+Cx + {\displaystyle \sum_{n=0}^\infty} \left[ \left(2(-1)^n\frac{x^{4n+3}}{(4n+3)}\right) \left( \frac{1}{4n+2}+1 \right) \right]
D
+
C
x
+
n
=
0
∑
∞
[
(
2
(
−
1
)
n
(
4
n
+
3
)
x
4
n
+
3
)
(
4
n
+
2
1
+
1
)
]
I don't know
Previous Part
Check Part 1
Next Part
Check Submission
More Functions and Power Series Questions:
Practice: Power Series Representation
Find a power series represetnation of
f
(
x
)
=
2
x
−
1
1
−
x
2
f(x)=\frac{2x-1}{1-x^2}
f
(
x
)
=
1
−
x
2
2
x
−
1
and determine the radius of convergece.
Practice: Power Series Representation
Practice: Power Series Representation
Find a power series represetnation of
f
(
x
)
=
2
x
−
1
1
−
x
2
f(x)=\frac{2x-1}{1-x^2}
f
(
x
)
=
1
−
x
2
2
x
−
1
and determine the radius of convergece.
Practice: Power Series Representation
Practice: Power Series Representation
Find a power series represetnation of
f
(
x
)
=
2
x
−
1
1
−
x
2
f(x)=\frac{2x-1}{1-x^2}
f
(
x
)
=
1
−
x
2
2
x
−
1
and determine the radius of convergece.
Practice: Power Series Representation
Practice: Power Series Representation
Find a power series represetnation of
f
(
x
)
=
2
x
−
1
1
−
x
2
f(x)=\frac{2x-1}{1-x^2}
f
(
x
)
=
1
−
x
2
2
x
−
1
and determine the radius of convergece.
Practice: Power Series Representation
Practice: Power Series Representation
Find a power series represetnation of
f
(
x
)
=
2
x
−
1
1
−
x
2
f(x)=\frac{2x-1}{1-x^2}
f
(
x
)
=
1
−
x
2
2
x
−
1
and determine the radius of convergece.
Practice: Power Series Representation
Practice: Power Series Representation
Find a power series represetnation of
f
(
x
)
=
2
x
−
1
1
−
x
2
f(x)=\frac{2x-1}{1-x^2}
f
(
x
)
=
1
−
x
2
2
x
−
1
and determine the radius of convergece.
Practice: Power Series Representation
Practice: Power Series Representation
Find a power series represetnation of
f
(
x
)
=
2
x
−
1
1
−
x
2
f(x)=\frac{2x-1}{1-x^2}
f
(
x
)
=
1
−
x
2
2
x
−
1
and determine the radius of convergece.