# 21B-B11.M2P - ◦ F per minute ±ind the time required for the temperature of the person to drop 40 ◦ F(ending up at 58 6 ◦ F 3(15 points ±ind

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Math 21B section B Winter 2011 Practice Midterm 2. Please do not use more than one page of notes, calculators or books. 1. (20 points) (Aracebo, Puerto Rico) A radio telescope dish is parabolic (the surface obtained by rotating a parabola y = kx 2 about the y axis) and has a radius of 1 hectometer and outer edge 1 2 hectometer higher than the center. (a) Write a deFnite integral for the surface area of the dish in square hectometers. (b) Write a deFnite integral for the work required to empty it if it is Flled with water to a depth of 1 8 hectometer (a quarter of the way to the rim) and the water must be pumped up to the rim. Write w for the weight density of the water in Newtons per cubic hectometer. 2. (10 points) Assume Newton’s Law of Cooling holds for a person who (start- ing at 98 . 6 F ) falls into 28 . 6 F arctic water. At the moment of immersion the temperature of the person drops at an instantaneous rate of 2

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Unformatted text preview: ◦ F per minute. ±ind the time required for the temperature of the person to drop 40 ◦ F (ending up at 58 . 6 ◦ F ). 3. (15 points) ±ind the most general solution to the following indeFnite in-tegrals: (a) i e √ x dx = (Hint: try substituting w = √ x ) (b) i x r 1-x 4 dx = (c) i dx x 2-1 = 4. (5 points) ±ind the following number: i x = π x =0 sin 2 ( x ) cos(2 x ) dx = 5. (5 points) (a) Estimate the number i x =1 x =0 e ( x 2 ) dx using the trapezoid rule with two intervals. (b) Find a bound for the error in your estimate. (Recall that the error for the trapezoid method using n intervals from a to b is bounded by M ( b − a ) 3 12 n 2 if the second derivative of the integrand is bounded in absolute value by M .)...
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## This note was uploaded on 05/26/2011 for the course MATH 16B taught by Professor Sarason during the Spring '06 term at University of California, Berkeley.

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21B-B11.M2P - ◦ F per minute ±ind the time required for the temperature of the person to drop 40 ◦ F(ending up at 58 6 ◦ F 3(15 points ±ind

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