Lydia is buying cupcake ls for he brother birthday party. She brought 36 cupcakes total.Of the cupcakes she bought,5/6 of them w
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Answer:
Step-by-step explanation:
Hi!
Lets call:
T = temprature of the object
T₀ = temperature of surroundings
t = time
The rate of change of T is its derivative with respecto to time. If T > T₀, the object looses heat, so T decreases. Then, being k > 0:
In this case T₀ = 70ºF and k = 0.05/min. Then the differential equation is:
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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