a. Factor, x 3 + 6 x 2 + 12 x + 8 (Hint: Use the rational zero theorem.) b. Find the partial fraction decomposition for 3 x 2 + 8 x − 5 x 3 + 6 x 2 + 12 x + 8 .
a. Factor, x 3 + 6 x 2 + 12 x + 8 (Hint: Use the rational zero theorem.) b. Find the partial fraction decomposition for 3 x 2 + 8 x − 5 x 3 + 6 x 2 + 12 x + 8 .
Solution Summary: The author explains how to calculate the factor form of the polynomial, x3+6 x +12x+8.
Evaluate the following integral over the Region R.
(Answer accurate to 2 decimal places).
√ √(x + y) A
R
R = {(x, y) | 25 < x² + y² ≤ 36, x < 0}
Hint: The integral and Region is defined in rectangular coordinates.
Find the volume of the solid that lies under the paraboloid z = 81 - x² - y² and within the cylinder
(x − 1)² + y² = 1. A plot of an example of a similar solid is shown below. (Answer accurate to 2
decimal places).
Volume using Double Integral
Paraboloid & Cylinder
-3
Hint: The integral and region is defined in polar coordinates.
Evaluate the following integral over the Region R.
(Answer accurate to 2 decimal places).
√4(1–2²
4(1 - x² - y²) dA
R
3
R = {(r,0) | 0 ≤ r≤ 2,0π ≤0≤¼˜}.
Hint: The integral is defined in rectangular coordinates. The Region is defined in polar coordinates.
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