Math 1560 Assignment 9 - cm 3 of liquid. Find the dimension...

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Mathematics 1560 Assignment 9 Due Date: November 26, 2010 1. A rectangular container with open top is to have a capacity of 100 m 3 . The length of the base has to be 4 times of the width. The cost for the bottom of the container is $20 per m 2 . Material for the sides cost $16 per m 2 . Find the cost of the cheapest container to be built. 2. A piece of wire 10 meter long is cut into two pieces. One piece is bent into a square and the other is bent into a square. How should the wire be cut so that the total area enclosed is (a) largest, (b) smallest. Please note that a zero cut is permitted. 3. A closed cylindrical can is made to contain 100
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Unformatted text preview: cm 3 of liquid. Find the dimension of the can with smallest surface area. 4. Find T 3 ( x ) (the Taylor polynomial of degree 3) for the function f at the number a . (a) f ( x ) = 1 x , a = 2 (b) f ( x ) = x + e-x , a = 0 5. Dierentiate the following functions. (a) y = sin( e x ) + e sin x (b) y = cos 1-e 2 x 1 + e 2 x ! (c) y = ln( x + x 2-1) (d) y = 2 3 x 2 (e) y = log 5 (1-3 e x ) 6. Find the absolute minimum value of the function f ( x ) = e x x on (0 , ). 7. Use denition to nd the area under the graph of f ( x ) = x 2 + x and above the x-axis on the interval [0 , 2]. 1...
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