In the following exercises, suppose that p ( x ) = ∑ n = 0 ∞ a n x n Satisfies lim n → ∞ a n + 1 a n = 1 where a n ≥ 0 for each n . State whether each series converges on the full interval (− 1, 1), or if there is not enough information to draw a conclusion. Use the comparison test when appropriate. 61. [T] Plot the graphs of the partial sums S N = ∑ n = 0 N ( − 1 ) n x 2 n + 1 ( 2 n + 1 ) ! For n =3, 5, 10 on the interval [ − 2 π , 2 π ] . Comment on the how these plots approximate sin x as N increases.
In the following exercises, suppose that p ( x ) = ∑ n = 0 ∞ a n x n Satisfies lim n → ∞ a n + 1 a n = 1 where a n ≥ 0 for each n . State whether each series converges on the full interval (− 1, 1), or if there is not enough information to draw a conclusion. Use the comparison test when appropriate. 61. [T] Plot the graphs of the partial sums S N = ∑ n = 0 N ( − 1 ) n x 2 n + 1 ( 2 n + 1 ) ! For n =3, 5, 10 on the interval [ − 2 π , 2 π ] . Comment on the how these plots approximate sin x as N increases.
In the following exercises, suppose that
p
(
x
)
=
∑
n
=
0
∞
a
n
x
n
Satisfies
lim
n
→
∞
a
n
+
1
a
n
=
1
where
a
n
≥
0
for each
n
. State whether each series converges on the full interval (− 1, 1), or if there is not enough information to draw a conclusion. Use the comparison test when appropriate.
61. [T] Plot the graphs of the partial sums
S
N
=
∑
n
=
0
N
(
−
1
)
n
x
2
n
+
1
(
2
n
+
1
)
!
For n =3, 5, 10 on the interval
[
−
2
π
,
2
π
]
. Comment on the how these plots approximate
sin
x
as N increases.
Q5: Discuss the stability critical point of the ODEs x + (*)² + 2x² = 2 and
draw the phase portrait.
(10M)
A retail store manager claims that the average daily sales of the store are $1,500.
You aim to test whether the actual average daily sales differ significantly from this claimed value.
You can provide your answer by inserting a text box and the answer must include:
Null hypothesis,
Alternative hypothesis,
Show answer (output table/summary table), and
Conclusion based on the P value.
Showing the calculation is a must. If calculation is missing,so please provide a step by step on the answers
Numerical answers in the yellow cells
.
The students who attend Memorial High School have a wide variety of extra-curricular activities to choose from in the after-school program. Students are 38% likely to join the dance team; 18% likely to participate in the school play; 42% likely to join the yearbook club; and 64% likely to join the marching band. Many students choose to participate in multiple activities. Students have equal probabilities of being freshmen, sophomores, juniors, or seniors.What is the probability of the union of being either a freshman or senior?
0.07
0.44
0.50
0.25
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