Finding the Interval of Convergence In Exercises 15–38, find the Interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.) ∑ n = 1 ∞ 2 ⋅ 3 ⋅ 4 ⋅ ⋅ ⋅ ( n + 1 ) x n n !
Finding the Interval of Convergence In Exercises 15–38, find the Interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.) ∑ n = 1 ∞ 2 ⋅ 3 ⋅ 4 ⋅ ⋅ ⋅ ( n + 1 ) x n n !
Solution Summary: The author explains how to calculate the interval of convergence of power series.
Finding the Interval of Convergence In Exercises 15–38, find the Interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.)
Find the volume of the solid bounded below by the circular cone z = 2.5√√√x² + y² and above by the
sphere x² + y²+z² = 6.5z.
Electric charge is distributed over the triangular region D shown below so that the charge density at (x, y)
is σ(x, y) = 4xy, measured in coulumbs per square meter (C/m²). Find the total charge on D. Round
your answer to four decimal places.
1
U
5
4
3
2
1
1
2
5
7
coulumbs
Let E be the region bounded cone z = √√/6 - (x² + y²) and the sphere z = x² + y² + z² . Provide an
answer accurate to at least 4 significant digits. Find the volume of E.
Triple Integral
Spherical Coordinates
Cutout of sphere is for visual purposes
0.8-
0.6
z
04
0.2-
0-
-0.4
-0.2
04
0
0.2
0.2
x
-0.2
04 -0.4
Note: The graph is an example. The scale and equation parameters may not be the same for your
particular problem. Round your answer to 4 decimal places.
Hint: Solve the cone equation for phi.
* Oops - try again.
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