MATH 0804 UC Davis

21D Mini Practice Exam 1 Solutions 1. Consider the cylinder x2 + y 2 = 25 bounded above by the plane z = 4 and below by the plane 2 2 z = 4 with density (x, y, z) = ex +y . a. What is the mass of the cylinder? (Hint: Change to a different coordinate

Problem: Set up the integral for the volume of the solid bounded above by the sphere z = 18 x2 y 2 and below by the cone z = x2 + y 2 in all three coordinate systems. Note this solid looks like an ice cream cone. Cartesian: We already have the z-

Problem: Set up the integral for the volume of the solid bounded above by the sphere z = 18 x2 y 2 and below by the cone z = x2 + y 2 in all three coordinate systems. Note this solid looks like an ice cream cone. Cartesian: We already have the z-

21D Mini Practice Exam 1 Solutions 1. Consider the cylinder x2 + y 2 = 25 bounded above by the plane z = 4 and below by the plane 2 2 z = 4 with density (x, y, z) = ex +y . a. What is the mass of the cylinder? (Hint: Change to a different coordinate

Sample Problems for Midterm III MAT 21B 1)(True/False) Label the following statements as either true or false. (No explanation required. Each correct label is worth two points.) a: ln(2 + 3) = ln2 + ln3 b: e6 = (e3 )2 c: eln(x-y) = elnx - elny d:

Sample Problems for Midterm II MAT 21B 1)(True/False) Label the following statements as either true or false. (No explanation required. Each correct label is worth two points.) a: 4 2 1 cot(t)dt = ln2 2 b: The center of mass is a force on a th