122test3 - Recognize each differential equation as...

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December 1, 2011 Math 122 - Test 3 Name__________________ Show work for full credit. Differentiate each function. 1. f x x x x ( ) sin sin sin = + + 2 2 2 2. f t t t ( ) cos = 2 Find each integral. 3. 12 2 0 4 cos x dx ! " 4. x x dx 2 cos " [ Hint : By parts.] 5. Find the area under the curve y x x = sin cos 2 and above the x -axis from x = 0 to x = ! 2. [ Hint : Use substitution to evaluate the integral representing the area.] ! /6 ! /3 ! /2 y x x = sin cos 2
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December 1, 2011 Math 122 - Test 3 page 2 of 4 6. Suppose you deposit $100 at the end of each month for 60 months into an account that earns interest at the rate of 6% per year (i.e. 0 06 12 0 005 . . = per month), compounded monthly. What is the value of the account after 60 months. Hint : The value can be described by the geometric series 100 1 005 100 100 1 005 100 1 005 100 1 005 0 59 2 59 ( . ) ( . ) ( . ) ( . ) j j = # = + + + $$$ + . Find the general solution of each separable differential equation. 7. % = y xy 2 2 8. % = & y e x 6 2
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December 1, 2011 Math 122 - Test 3
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Unformatted text preview: Recognize each differential equation as determining unlimited, limited, or logistic growth, and then solve. 9. % = = y y y 0 25 4 . ( ) 10. % = & = y y y 5 20 ( ) ( ) 11. % = & = y y y y 1 2 2 1 ( ) ( ) ****************************************************************************** Formulas Differential Equation Solution Unlimited growth % = y ay y ce at = Limited growth % = & y a M y ( ); y ( ) = y M e at = & & ( ) 1 Logistic growth % = & y ay M y ( ) y M ce aMt = + & 1 Trigonometry sin cos 2 = = ! ; sin cos 2 1 = = December 1, 2011 Math 122 - Test 3 page 4 of 4 Solve the first-order linear differential equations and, where applicable, initial condition. 12. % + = y y x 3 13. xy y x % + = 4 7 3 14. % + = = & y y e y x 4 4 3 ( )...
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