20b_04f_fe

20b_04f_fe - Math 20B Final Exam 80 points Fall 2004 Print...

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Math 20B Final Exam 80 points Fall 2004 Print Name, ID number and Section on your blue book. BOOKS and CALCULATORS are NOT allowed. One page of notes (both sides) is allowed. You must show your work to receive credit. 1. (24 pts.) For each of the following integrals, either evaluate the integral or prove that it diverges. You may leave complex numbers in your answers. (a) i 9 0 dx 1 + x (b) i cos 2 x e x dx (c) i x r 1 - x 2 dx (d) i 1 1 dx x 2 2. (9 pts.) Consider the di±erential equation dy/dt = y (2 + y )(3 - y ). (a) Find all constants A such that y ( t ) = A is a solution to the di±erential equation. You must brie²y explain how you determined the values. (b) If the initial condition is y (0) = 4, what is lim t →∞ y ( t )? You must brie²y explain why. (c) If the initial condition is y (0) = - 1, what is lim t →∞ y ( t )? You must brie²y explain why. Note: An answer to (b) or (c) might be
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20b_04f_fe - Math 20B Final Exam 80 points Fall 2004 Print...

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