Francesca bought a rectangular piece of fabric that is 2/3 yard long and 3/4 yard wide. What is the area, in square yards, of th
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For this case, the first thing we must do is define variables.
We have then:
x: number of pens
y: number of pencils
We now write the system of inequations:
The solution to the system of inequations is given by the shaded region.
Note: see attached image.
We have then:
x: number of pens
y: number of pencils
We now write the system of inequations:
The solution to the system of inequations is given by the shaded region.
Note: see attached image.
The radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series. This can be obtained by using ratio test.
<h3>Find the radius of convergence R and the interval of convergence:</h3>Ratio test is the test that is used to find the convergence of the given power series.
First aₙ is noted and then aₙ₊₁ is noted.
For ∑ aₙ, aₙ and aₙ₊₁ is noted.
= β
- If β < 1, then the series converges
- If β > 1, then the series diverges
- If β = 1, then the series inconclusive
Here =
and
=
Now limit is taken,
=
=
=
=
= < 1
- 1 < < 1
- 1 - 2 < x < 1 - 2
- 3 < x < - 1
We get that,
interval of convergence = (-3, -1)
radius of convergence R = 1
Hence the radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series.
Learn more about radius of convergence here:
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