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test_2_sample_10

# test_2_sample_10 - bounded by the lines x = 0 y = 0 and 2 x...

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MATH 251 section 502, Sample Test #2 , Fall 2010 Name ..................................................... Closed book, no notes, calculators OK. Show the whole work. Solve the following problems for total 100 pts. Each problem is worth of 10 points. There a possibility to have also a bonus problem. 1. Exercises 12.7, Problem 26 (or 31). 2. A package in the shape of a rectangular box can be mailed parcel post if the sum of the length and girth (i.e. the perimeter of the cross-section perpendicular to the length) is at most 84 in. Find the dimensions of the package with largest volume that can be mailed parcel post. 3. Problem 15, Section 12.8 (page 788 of your book). 4. Find the volume of the solid lying under the paraboloid z = x 2 + 4 y 2 and above the domain
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Unformatted text preview: bounded by the lines x = 0, y = 0, and 2 x + y = 2. 5. Find the volume of the solid lying under the plane z = 2 x + 4 y + 1 and above the rectangle { ( x,y ) :-1 ≤ x ≤ , 1 ≤ y ≤ 4 } . 6. Exercises 13.5, Problem 17. 7. Given the region D in the ﬁrst quadrant and between the circles x 2 + y 2 = 4 and x 2 + y 2 = 2 x . Evaluate the integral RR D ydA. 8. Rewiew of Chapter 13, Problem 67. 9. Find the mass of the lamina of density ρ = 3 that occupies the area D bounded by the parabola x = y 2 and the line y = x-2. 10. Find surface area of the part of the sphere x 2 + y 2 + z 2 = 4 that lies above the plane z = 1. 11. (if we get to that point) Problem 10, section 13.8, page 843....
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