Congratulations! You passed!
Grade received 62.50%
Latest Submission Grade 62.50%
To pass 60% or higher
Go to next item
1.
Question 1
Find all possible solutions to the equation
=
��� �
e
ix
=
i
.
1 / 1 point
Correct
2.
Question 2
Calculate
∑
=0∞(−1)
(ln 4)
!
�
�
��
k
=0
∑
∞
(−1)
k
k
!(ln4)
k
.
1 / 1 point
Correct
3.
Question 3
Calculate
∑
=0∞(−1)
2
(2
)!
�
�� �
�
k
=0
∑
∞
(−1)
k
(2
k
)!
π
2
k
.
0 / 1 point
Incorrect
4.
Question 4
Write out the first four terms of the sum
∑
=1∞(−1)
+12
2
−1
�
�
� �
k
=1
∑
∞
2
k
−1(−1)
k
+1
2
k
.
1 / 1 point
Correct
5.
Question 5
Write out the first four terms of the sum
∑
=0∞(−1)
2
!(2
+1)
�
�� ��
�
k
=0
∑
∞
k
!(2
k
+1)
(−1)
k
π
2
k
.
1 / 1 point
Correct
6.
Question 6
Which of the following expressions describes the sum
2−
24+
36−
48+
�
�
�
�
⋯
2
e
−4
e
2
+6
e
3
−8
e
4
+
⋯
?
0 / 1 point
Incorrect
7.
Question 7
Which of the following expressions describes the sum
−1+
2
�
⋅
1−
23
�
⋅
2
⋅
1+
34
�
⋅
3
⋅
2
⋅
1+
⋯
−1+2
⋅
1
x
−3
⋅
2
⋅
1
x
2
+4
⋅
3
⋅
2
⋅
1
x
3
+
⋯
?
1 / 1 point
Correct
8.
Question 8
Engineers and scientists sometimes use powers of 10 and logarithms in base 10. In mathematics,
we tend to prefer exponentials with base
�
e
and natural logarithms. We have seen in lecture one
of the main reasons: the derivative of the exponential function
��
e
x
is itself. For applications, it is
