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Unformatted text preview: Practice Problem for Midterm #1, Math 1502 1. The population of a country grows at a rate proportional to the current population. Numerical data show that the proportionality factor is 4% per year. Let P ( t ) be the population of this country at time t . (a) Write down the differential equation for P ( t ). (b) Find a formula for P ( t ). (c) How many years does it take for the population of this country to double? Find the exact formula. 2. Solve the following initial value problems: (a) 2 ty + t 2 y = t 2 , y (0) = 4 (b) dy dx = x 2 y (1+ x 3 ) , y (0) =- 3 3. Find the following limits. Show your work/reasoning! (a) lim t → 1 t 3- 1 t 2- 1 (b) lim t →∞ t ( e 2 /t- 1 ) (c) lim x → e x x (d) lim x →∞ ( cos 1 x ) x 3. Find the general solution to the following differential equations: (a) y 00- 2 y- 3 y = 0 (b) y 00 + 8 y + 16 y = 0 (c) y + 2 t y = cos t t 2 4. Determine if the integral converges and, if so, calculate the integral. Show your work/reasoning!...
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This note was uploaded on 02/26/2012 for the course CHBE 2100 taught by Professor Staff during the Spring '08 term at Georgia Tech.
- Spring '08