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1.
Question 1
Compute the Taylor series about
=0
�
x
=0
of the polynomial
(
)=
4+4
3+
2+3
+6
� �
�
�
�
�
f
(
x
)=
x
4
+4
x
3
+
x
2
+3
x
+6
. Be sure to fully simplify. What does this
tell you about the Taylor series of a polynomial?
Hint:
If you paid attention during the lecture, this will be a very simple problem!
1 / 1 point
Correct
2.
Question 2
Compute the first three terms of the Taylor series about
=0
�
x
=0
of
1+
�
1+
x
.
1 / 1 point
Correct
3.
Question 3
Find the first four non-zero terms of the Taylor series about
=0
�
x
=0
of the function
(
+2)−1
�
(
x
+2)
−1
.
1 / 1 point
Correct
4.
Question 4
Compute the coefficient of the
3
�
x
3
term in the Taylor series about
=0
�
x
=0
of the function
−2
�
�
e
−2
x
.
1 / 1 point
Correct
5.
Question 5
Which of the following is the Taylor series about
=0
�
x
=0
of
11−
�
1−
x
1
?
0 / 1 point
Incorrect
6.
Question 6
What is the derivative of the Bessel function
0(
)
�
�
J
0
(
x
)
at
=0
�
x
=0
? Remember that
0(
)
�
�
J
0
(
x
)
is defined through its Taylor series about
=0
�
x
=0
:
0(
)=∑
=0∞(−1)
2
22
(
!)2
�
�
�
�� �
� �
J
0
(
x
)=
k
=0
∑
∞
(−1)
k
2
2
k
(
k
!)
2
x
2
k
1 / 1 point
Correct
