We can use the fact that, for 
,
Notice that
![\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1{1-x}\right]=\dfrac1{(1-x)^2}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5B%5Cdfrac1%7B1-x%7D%5Cright%5D%3D%5Cdfrac1%7B%281-x%29%5E2%7D)
so that
![f(x)=\displaystyle\frac5{(1-x)^2}=5\frac{\mathrm d}{\mathrm dx}\left[\sum_{n=0}^\infty x^n\right]](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdisplaystyle%5Cfrac5%7B%281-x%29%5E2%7D%3D5%5Cfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5B%5Csum_%7Bn%3D0%7D%5E%5Cinfty%20x%5En%5Cright%5D)
By the ratio test, this series converges if
so the series has radius of convergence 
.
Step-by-step explanation:
how do you write over the thing so I can give you the answer or can I just tell you the answer in text messages
Answer:
Option B
Step-by-step explanation:
Given that a candy manufacturer is interested in the distribution of colors in each of its packages of candy sold. The manufacturer randomly sample packages from multiple batches at one factory.
Because he resorts to only one factory, there may be bias in the sample. Other factories may have different processes of the settings and also if a diversified sample is taken then it is likely to represent the whole population, and hence results would be more accurate
Option A is incorrect since only one factory was done
C and D are not selected because one factory result cannot be generalised to all other factors in the same country or outside.
So answer would be
B) No, because the other factories may have different processes or the settings
Answer:
12 times.
Step-by-step explanation:
If she swims three times a week, then you need to find how many weeks make up 28 days. 28/7= 4 weeks. Since she swims three times a week, you multiple that by the amount of weeks, which is four. You get that she swims 12 times in 28 days.
Given two numbers x and y such that:
x + y = 12 ... (1)
<span>two numbers will maximize the product g</span>
from equation (1)
y = 12 - x
Using this value of y, we represent xy as
xy = f(x)= x(12 - x)
f(x) = 12x - x^2
Differentiating the above function:
f'(x) = 12 - 2x
Maximum value of f(x) occurs at point for which f'(x) = 0.
Equating f'(x) to 0 we get:
12 - 2x = 0
2x = 12
> x = 12/2 = 6
Substituting this value of x in equation (2):
y = 12 - 6 = 6
Therefore, value of xy is maximum when:
x = 6 and y = 6
The maximum value of xy = 6*6 = 36
