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ayoismeisjjjjuan
13.03.2020 •
Mathematics
(1 point) The series ∑Cn(x+4)n converges at x=0 and diverges at x=−11. Based on this information we know something about how big and small the radius of convergence R of the power series can be. Between what two values must R lie?
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Ответ:
Following are the calculation of the value that lie on R:
Given:
converges at![x=0](/tpl/images/0545/8043/37eb6.png)
diverges at![x=-11](/tpl/images/0545/8043/406cd.png)
To find:
Find the value of R that lie=?
Solution:
When
When
So,
Therefore, the answer is "
".
Learn more:
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Ответ:
R must lie between the two values 4 and 7
R ∈ (4,7)
Step-by-step explanation:
∑![C_{n}](/tpl/images/0545/8043/2b669.png)
![(x+4)^{n}](/tpl/images/0545/8043/ce4ec.png)
converges at x= 0 and Diverges at x= -11
Given series is centered at x= -4
since the series converges at x= 0, which is a distance of 4 from x= -4
=> the radius of convergence (R) is at least 4
since the series diverges at x= -11, which is a distance of 7 from x= -4
=> the radius of convergence (R) cannot be more than 7
=> 4 ≤ R ≤ 9 ⇒ R ∈ (4,7)
Ответ:
a) 48
b) 37
Step-by-step explanation:
a) 16 and 64 is
and ![8^{2}](/tpl/images/2519/2620/b648a.png)
64-16=48
b) 27 and 64 is
and ![4^{3}](/tpl/images/2519/2620/13a8f.png)
64-27=37