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assignment 2

# assignment 2 - ρ x = 1 0 2 × 10-8 x 2(240-x where ρ is...

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Calculus for the life Sciences II MAT 1332B, MAT 1332C Assignment 2 Due date: 8:30 in class, January 27, 2010 Instructor (circle one): Robert Smith? , Jing Li DGD (circle one): 1, 2, 3, 4 Student Name (printed) Student Number By signing below, you declare that this work was your own and that you have not copied from any other individual or other source. Signature 1. Find the area between f ( x ) = sin(2 x ) and g ( x ) = cos(2 x ) for 0 x π . (Hint: Sketch the curves.) 2. Suppose that energy is produced at a rate of E ( t ) = 360 t - 39 t 2 + t 3 where E is measured in joules per hour and t is measured in hours. Find the total energy generated from t = 0 to t = 24. (Hint: The rate is zero at times t = 0, 15 and 24.) 3. Consider a snake that is 2 metres long, with a density described by
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Unformatted text preview: ρ ( x ) = 1 . 0 + 2 . × 10-8 x 2 (240-x ) where ρ is measured in grams per centimetre and x is measured in centimetres from the tip of the tail. (a) Find the minimum density of the snake. (b) Find the maximum density of the snake. (c) Where does the maximum occur? (d) Find the total mass of the snake. (e) Find the average density of the snake. (f) How does the average density compare with the minimum and maxi-mum? (g) Graph the density and average. 4. Find the volume obtained by rotating f ( x ) = sin ‡ x 4 · around the x-axis, between-π and π . 1...
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