Answer:
Step-by-step explanation:
a) ![\int\limits^{\infty} _1 {\frac{1}{n^4} } \, dn\\ =\frac{n^{-3} }{-3}](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%7B%5Cinfty%7D%20_1%20%7B%5Cfrac%7B1%7D%7Bn%5E4%7D%20%7D%20%5C%2C%20dn%5C%5C%20%3D%5Cfrac%7Bn%5E%7B-3%7D%20%7D%7B-3%7D)
Substitute limits to get
= ![\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D)
Thus converges.
b) 10th partial sum =
![\int\limits^{10} _1 {\frac{1}{n^4} } \, dn\\ =\frac{n^{-3} }{-3}](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%7B10%7D%20_1%20%7B%5Cfrac%7B1%7D%7Bn%5E4%7D%20%7D%20%5C%2C%20dn%5C%5C%20%3D%5Cfrac%7Bn%5E%7B-3%7D%20%7D%7B-3%7D)
=![\frac{-1}{3} (0.001-1)\\= 0.333](https://tex.z-dn.net/?f=%5Cfrac%7B-1%7D%7B3%7D%20%280.001-1%29%5C%5C%3D%200.333)
c) Z [infinity] n+1 1 /x ^4 dx ≤ s − sn ≤ Z [infinity] n 1 /x^ 4 dx, (1)
where s is the sum of P[infinity] n=1 1/n4 and sn is the nth partial sum of P[infinity] n=1 1/n4 .
(question is not clear)
Answer:
the answer is b, 12
Step-by-step explanation:
16-4=12
Answer:
3
Step-by-step explanation:
I used a graph
Step-by-step explanation:
7x + 8y = -12
8y=-12-7x
y=
![\frac{ - 12 - 7 x}{8}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20-%2012%20-%207%20x%7D%7B8%7D%20)