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1.
Question 1
What is the domain of the function
(
)=ln
� �
�
f
(
x
)=ln
x
?
1 / 1 point
Correct
2.
Question 2
Which of the following is the Taylor series of
ln11−
�
ln1−
x
1
about
=0
�
x
=0
up to and including
the terms of order three?
1 / 1 point
Correct
3.
Question 3
Using your knowledge of Taylor series, find the sixth derivative
(6)(0)
�
f
(6)
(0)
of
(
)=
−
2
� �
� �
f
(
x
)=
e
−
x
2
evaluated at
=0
�
x
=0
.
1 / 1 point
Correct
4.
Question 4
Recall that the Taylor series for
arctanarctan
is
arctan
=∑
=0∞(−1)
2
+12
+1
�
�
�� �
�
arctan
x
=
k
=0
∑
∞
(−1)
k
2
k
+1
x
2
k
+1
for
∣
�
∣
<1
∣
x
∣
<1
. Using this, compute
lim
→0arctan
3+7
�
��
�
x
→0
lim
x
3
+7
x
arctan
x
.
0 / 1 point
Incorrect
5.
Question 5
lim
→0cos3
−cos5
2=
�
�
��
x
→0
lim
x
2
cos3
x
−cos5
x
=
1 / 1 point
Correct
6.
Question 6
Determine which value is approximated by
1+2
+
2+(2
)33!+(2
)44!+(2
)55!+H.O.T.
� �
�
�
�
1+2
π
+
π
2
+3!(2
π
)
3
+4!(2
π
)
4
+5!(2
π
)
5
+H.O.T.
0 / 1 point
Incorrect
7.
Question 7
Which of the following expressions describes the sum
