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1.
Question 1
Use a Taylor series to find a good quadratic approximation
to 2
2
� �
e
2
x
2
near =0
�
x
=0
. That means, use the terms in the Taylor series up to an including degree two.
1 / 1 point
Correct
2.
Question 2
Determine the Taylor series of 2+
��
�
e
u
2
+
u
up to terms of degree four.
0 / 1 point
Incorrect
3.
Question 3
Compute the Taylor series expansion of 1−cos
�
�
e
1−cos
x
up to and including terms of degree four.
0 / 1 point
Incorrect
4.
Question 4
Compute the first three nonzero terms of the Taylor series of cos(sin
)
�
cos(sin
x
)
.
1 / 1 point
Correct
5.
Question 5
Compute the first three nonzero terms of the Taylor series of cos(2
)−1
2
�
�
x
2
cos(2
x
)−1
.
1 / 1 point
Correct
6.
Question 6
Determine the Taylor series expansion of cos
sin2
�
�
cos
x
sin2
x
up to terms of degree five. Hint:
don't start computing derivatives!
1 / 1 point
Correct
7.
Question 7
Compute the Taylor series expansion of −1
sin
�
��
�
x
−1
e
x
sin
x
up to and including terms of degree four.
1 / 1 point
Correct
8.
Question 8
Determine the first three nonzero terms of the Taylor expansion of 2
sinh
2
� �
� �
2
xe
2
x
sinh
x
.
0 / 1 point
