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Practice: Taylor Series
Related Topics
Wize University Calculus 2 Textbook > Power Series
Taylor and Maclaurin Series
7 Activities
Practice Question
Find the Taylor series representation for
f
(
x
)
=
1
1
+
2
x
f(x)=\frac{1}{1+2x}
f
(
x
)
=
1
+
2
x
1
about
c
=
−
2
c=-2
c
=
−
2
. Then, state the radius of convergence.
f
(
x
)
=
−
∑
n
=
0
∞
2
n
3
n
+
1
(
x
+
2
)
n
\displaystyle f(x)=-{\displaystyle \sum_{n=0}^\infty} \frac{2^n}{3^{n+1}}(x+2)^n
f
(
x
)
=
−
n
=
0
∑
∞
3
n
+
1
2
n
(
x
+
2
)
n
Radius of convergence is
R
=
1
2
R=\frac{1}{2}
R
=
2
1
f
(
x
)
=
−
∑
n
=
0
∞
2
n
3
n
+
1
(
x
+
2
)
n
\displaystyle f(x)=-{\displaystyle \sum_{n=0}^\infty} \frac{2^n}{3^{n+1}}(x+2)^n
f
(
x
)
=
−
n
=
0
∑
∞
3
n
+
1
2
n
(
x
+
2
)
n
Radius of convergence is
R
=
3
2
R=\frac{3}{2}
R
=
2
3
f
(
x
)
=
∑
n
=
0
∞
2
n
3
n
(
x
+
2
)
n
\displaystyle f(x)={\displaystyle \sum_{n=0}^\infty} \frac{2^n}{3^{n}}(x+2)^n
f
(
x
)
=
n
=
0
∑
∞
3
n
2
n
(
x
+
2
)
n
Radius of convergence is
R
=
1
2
R=\frac{1}{2}
R
=
2
1
f
(
x
)
=
∑
n
=
0
∞
2
n
3
n
(
x
+
2
)
n
\displaystyle f(x)={\displaystyle \sum_{n=0}^\infty} \frac{2^n}{3^{n}}(x+2)^n
f
(
x
)
=
n
=
0
∑
∞
3
n
2
n
(
x
+
2
)
n
Radius of convergence is
R
=
3
2
R=\frac{3}{2}
R
=
2
3
f
(
x
)
=
−
∑
n
=
0
∞
2
n
+
1
3
n
+
1
(
x
+
2
)
n
\displaystyle f(x)=-{\displaystyle \sum_{n=0}^\infty} \frac{2^n+1}{3^{n+1}}(x+2)^n
f
(
x
)
=
−
n
=
0
∑
∞
3
n
+
1
2
n
+
1
(
x
+
2
)
n
Radius of convergence is
R
=
1
2
R=\frac{1}{2}
R
=
2
1
I don't know
Check Submission
More Taylor and Maclaurin Series Questions:
Practice: Taylor Series
Find the Taylor series representation for
f
(
x
)
=
1
1
+
2
x
f(x)=\frac{1}{1+2x}
f
(
x
)
=
1
+
2
x
1
about
c
=
−
2
c=-2
c
=
−
2
. Then, state the radius of convergence.
Practice: Taylor Series
Find the Taylor series representation for
f
(
x
)
=
1
1
+
2
x
f(x)=\frac{1}{1+2x}
f
(
x
)
=
1
+
2
x
1
about
c
=
−
2
c=-2
c
=
−
2
. Then, state the radius of convergence.
Practice: Taylor Series
Practice Question
Find the Taylor series representation for
f
(
x
)
=
1
1
+
2
x
f(x)=\frac{1}{1+2x}
f
(
x
)
=
1
+
2
x
1
about
c
=
−
2
c=-2
c
=
−
2
. Then, state the radius of convergence.
Practice: Taylor Series
Practice Question
Find the Taylor series representation for
f
(
x
)
=
1
1
+
2
x
f(x)=\frac{1}{1+2x}
f
(
x
)
=
1
+
2
x
1
about
c
=
−
2
c=-2
c
=
−
2
. Then, state the radius of convergence.
Practice: Taylor Series
Practice Question
Find the Taylor series representation for
f
(
x
)
=
1
1
+
2
x
f(x)=\frac{1}{1+2x}
f
(
x
)
=
1
+
2
x
1
about
c
=
−
2
c=-2
c
=
−
2
. Then, state the radius of convergence.
Which of the following is the coefficient for
x
8
x^8
x
8
in the MacLaurin series for the function
f
(
x
)
=
cos
(
5
x
)
f(x) = \cos(5x)
f
(
x
)
=
cos
(
5
x
)
?