Assignment4

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MATH1821 Mathematical Methods for Actuarial Science I Assignment 4 Due date: 4 November, 2016 1. The figure below shows two right circular cones, one upside down inside the other. The two bases are parallel, and the vertex of the smaller cone lies at the center of the larger cone’s base. What values of r and h will give the smaller cone the largest possible volume? 2. What is the length of the longest ladder you can carry horizontally around the corner of the corridor shown below? 3. Prove that x 0 (∫ u 0 f ( t ) dt ) du = x 0 f ( u )( x - u ) du. ( Hint: Express the integral on the right-hand side as the difference of two integrals. Then show that both sides of the equation have the same derivative with respect to x .) 4. The graph of a function f consists of a semicircle and two line segments as shown. Let
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