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1b-2009-final_exam_sample_2

# 1b-2009-final_exam_sample_2 - In an isolated town of 5000...

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Math 1B — Sample Final #2 Fall Program for Freshmen 2009 Fred Bourgoin 1. Evaluate each integral. (a) Z cos x 4 - sin 2 x dx (b) Z π/ 2 0 cos 3 θ sin θ dθ 2. Determine whether the series X n =2 1 n ln n converges or diverges. 3. Evaluate Z 4 0 ln x x dx or show that it is divergent. 4. Consider the integral Z 4 0 f ( x ) dx , where f ( x ) = x 2 + 1. [Note that f 00 ( x ) = ( x 2 + 1) - 3 / 2 .] (a) If we use n = 4, which is more likely to give a better approximation: the midpoint rule or the trapezoidal rule? Why? (b) Approximate the integral using the rule you chose in part (a). (c) What is the maximum error of your approximation? 5. Find the exact value of Z 1 0 x 2 + 1 dx . 6. Solve the initial-value problem: dr dt + 2 tr = r, r (0) = 5 . 7. One model for the spread of an epidemic is that the rate of spread is jointly pro- portional to the number of infected people and the number of uninfected people.

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Unformatted text preview: In an isolated town of 5000 inhabitants, 160 have a disease at the beginning of the week and 1200 have it at the end of the week. How long does it take for 80% of the population to become infected? [Advice: Measure time in weeks.] 8. Use Maclaurin series to approximate Z 1 √ 1 + x 4 dx with | error | < . 01. 9. Find the interval of convergence of ∞ X n =1 2 n ( x-2) n 2 n + 1 . 10. Solve y 00-y-6 y = e 3 t + t + 1. 1 11. Solve y 00 + y = 3 cos t using a diﬀerent method than the one you used in the preceding problem. 12. Solve y 00-2 xy-4 y = 0 using a method you haven’t used in the preceding two problems. 2...
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1b-2009-final_exam_sample_2 - In an isolated town of 5000...

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