Clara Gepner
01
WeBWorK assignment due : 04/16/2023 at 11:59pm EDT.
5. (1 point)
Suppose that
1. (1 point)
∞
6x
Represent the function
as a power series f (x) =
6+x
∞
8
= ∑ cn x n
(15 + x) n=0
∑ cn xn
n=0
Find the following coefficients of the power series.
c0 =
c0 =
c1 =
c1 =
c2 =
c2 =
c3 =
c3 =
c4 =
c4 =
Find the radius of convergence R =
.
Find the radius of convergence R of the power series.
R=
.
2. (1 point)
Find the convergence set of the given power series:
6. (1 point)
The function f (x) =
(x − 2)n
∑ n2
n=1
∞
The above series converges for
3
1+64x2
is represented as a power series
∞
f (x) =
≤x≤
.
∑ cn x n .
n=0
Find the first few coefficients in the power series.
3. (1 point) Find all the values of x such that the given series
would converge.
c0 =
c1 =
(6x)n
∑ 5
n=1 n
∞
c2 =
c3 =
Answer:
c4 =
Note: Give your answer in interval notation.
Find the radius of convergence R of the series.
R=
.
4. (1 point) Find all the values of x such that the given series
would converge.
Z x
7. (1 point) Let F(x) =
sin(8t 2 ) dt.
0
Find the MacLaurin polynomial of degree 7 for F(x).
(x − 7)n
7n
n=1
∞
∑
Use
Answer:
Z 0.73
this
2
polynomial
sin(8x ) dx.
0
Note: Give your answer in interval notation
1
to
estimate
the
value
of
∞
Note: your answer to the last part needs to be correct to 9
decimal places.
2.
n=0
∞
(−1)n 22n x2n
(2n)!
n=0
∞
2n x n
4. ∑
n=0 n!
8. (1 point)
Find Taylor series of function f (x) = ln(x) at a = 3.
∞
( f (x) =
∑ cn (x − 3)n )
n=0
c0 =
c1 =
c2 =
3.
∑
A.
B.
C.
D.
cos(2x)
e2x
2 sin(x)
2 arctan(x)
10. (1 point)
Find the Maclaurin series of the function f (x) = (2x2 )e−5x .
c3 =
∞
c4 =
f (x) =
Determine the following coefficients:
c1 =
The series is convergent:
, left end included (Y,N):
from x =
to x =
, right end included (Y,N):
c2 =
c3 =
9. (1 point)
Match each of the Maclaurin series with correct function.
∞
∑
n=0
∑ cn xn
n=0
Find the interval of convergence.
1.
2x2n+1
∑ (−1)n (2n + 1)!
c4 =
(−1)n 2x2n+1
c5 =
2n + 1
Generated by c WeBWorK, http://webwork.maa.org, Mathematical Association of America
2