finalexam_map2302-69870_dj_s09

finalexam_map2302-69870_dj_s09 - TALLAHASSEE COMMUNITY...

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Unformatted text preview: TALLAHASSEE COMMUNITY COLLEGE MAP 2302 – 69870 // SUMMER 2009 CUMULATIVE FINAL EXAM INSTRUCTOR: D. JONES LAST ________________ , FIRST ______________ THURS. 16 JUL 09 // 9:00 am – 10:45 am // AC 112 ZILL’s CLASSIC 5‐th // CHs 1, 2, 3.2, 4, 5.1, 5.2, 7.1‐7.5 Problems #1, 4, 5, and 8 are 12 points each. Problems 2, 3, 6, and 7 are 13 points each. The Bonus is 10 points. =============================================================================================== #1/ Verify that y1 = 2e − 4 x is a solution of #2/ State explicitly the method you are using and solve: y dx + (1 + x ) dy = 0 . Assume x > 0 and y > 0. y′′ + 3 y′ − 4 y = 0 . #3/ Initially 80 lbs. of salt are dissolved into a large tank holding 400 gal. of water. A brine solution is pumped into the tank at the rate of 2 gal. per min., and the well‐stirred solution is then pumped out at the same rate. If the concentration of the salt solution entering is 0.5 pounds per gallon, [A] determine the amount of salt in the tank at time t. Also,[B] approximately how much salt is in the tank after ten hours? [ For part [B] give complete approximate calculator answer and then round your final answer to the nearest pound. Write sentence for final answer. ] #4/ Verify that the operator ( D − 1)( D + 3) annihilates the function #5/ Are these functions linearly dependent or linearly independent? Show why. f 1 ( x ) = 3 x − 4, f 2 ( x ) = 4 x − 8, f 3 ( x ) = 10 x − 13. 4e x + 5e − 3 x . #6/ A 16‐lb weight attached to a spring exhibits simple harmonic motion. There is no damping. Determine the equation of motion if the spring constant is 4 lb/ft and if the weight is released 2 ft below the equilibrium position with a downward velocity of 1 ft/sec. (Assume g = 32 ft sec 2 ). _______________________________________________________________________________________________ and y ( 0 ) = 0 and y′ ( 0 ) = 0. #7/ Solve this IVP using Laplace Transforms. y′′ + 4 y′ + 4 y = e − 2 t #8/ Find [ A ] L { f (t )} if f ( t ) = 4 − e − 3t sin t + cos 2t { } [ B ] L −1 F ( s ) if F ( s ) = s+2 s 2 + 16 if 0 ≤ t < 1 ⎧0 ⎪ #9(bonus) // Re‐write the given piecewise function in terms of unit step functions. f ( t ) = ⎨t 2 + 2 if 1 ≤ t < 5 ⎪0 if 5 ≤ t ⎩ finalexam_map2302-69870_dj_s09.doc Page 1 of 1 ...
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This note was uploaded on 12/30/2011 for the course MAP 2302 taught by Professor Jones during the Summer '11 term at Tallahassee Community College.

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