Answer:
1. In order to make the integral improper
must be 1.
2. In order to make the integral improper
must be 1.
Step-by-step explanation:
Using the rules of integration we get that for
![f(x)= \frac{1}{x^p}](https://tex.z-dn.net/?f=f%28x%29%3D%20%5Cfrac%7B1%7D%7Bx%5Ep%7D)
![\int\limits_{0}^{1} \frac{1}{x^p} \, dx = \frac{x^{1-p}}{(1-p)} \, |\limits_{0}^{1} = \frac{1}{1-p} - 0 = \frac{1}{1-p}](https://tex.z-dn.net/?f=%5Cint%5Climits_%7B0%7D%5E%7B1%7D%20%20%5Cfrac%7B1%7D%7Bx%5Ep%7D%20%20%5C%2C%20dx%20%20%3D%20%5Cfrac%7Bx%5E%7B1-p%7D%7D%7B%281-p%29%7D%20%20%5C%2C%20%7C%5Climits_%7B0%7D%5E%7B1%7D%20%20%20%3D%20%5Cfrac%7B1%7D%7B1-p%7D%20-%200%20%3D%20%5Cfrac%7B1%7D%7B1-p%7D)
Therefore in order to make that integral improper
must be 1.
If p = 1 then you would have a 1/0 indeterminate form.
2. Using the of integration, specifically substitution we get that for
![f(x) = \frac{1}{x(ln(x)^p)}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7B1%7D%7Bx%28ln%28x%29%5Ep%29%7D)
![\int\limits_{e}^{\infty} \frac{1}{x(ln(x))^p} \, dx = \frac{(ln(x))^{1-p}}{1-p} \, |\limits_{e}^{\infty}](https://tex.z-dn.net/?f=%5Cint%5Climits_%7Be%7D%5E%7B%5Cinfty%7D%20%5Cfrac%7B1%7D%7Bx%28ln%28x%29%29%5Ep%7D%20%5C%2C%20dx%20%20%3D%20%5Cfrac%7B%28ln%28x%29%29%5E%7B1-p%7D%7D%7B1-p%7D%20%5C%2C%20%7C%5Climits_%7Be%7D%5E%7B%5Cinfty%7D)
For
we would have
![\int\limits_{e}^{\infty} \frac{1}{x(ln(x))^p} \, dx = \frac{1}{p-1}](https://tex.z-dn.net/?f=%5Cint%5Climits_%7Be%7D%5E%7B%5Cinfty%7D%20%5Cfrac%7B1%7D%7Bx%28ln%28x%29%29%5Ep%7D%20%5C%2C%20dx%20%20%3D%20%5Cfrac%7B1%7D%7Bp-1%7D)
And the problem is the same. If
we would have a 1/0 indeterminate form.
Answer:
"the original amount of the loan"
Step-by-step explanation:
x value would be the time in months and y value would be the loan amount that is left.
The y-intercept is basically the point where x is 0. So, we can say the y-intercept would be when time is 0.
<em>That's basically when the loan started and the y-value represents the full loan amount., which is $22,000.</em>
<em />
The correct answer is third option -- "the original amount of the loan".
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Answer:
Negative Infinity
Step-by-step explanation:
It is a negative slope, therefore as x moves towards positive infinity, y will move towards negative infinity.
Answer:
exponent
Step-by-step explanation:
Answer:
T-X
Step-by-step explanation:
Today=T
Yesterday = X
To find the diffrence you need to subtract Today from Yesterday then you will get your answer