final_wi04

# final_wi04 - between tuneups 6(6 points The mass of a...

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Name: Section Number: TA Name: Section Time: Math 10B. Final Examination March 16, 2004 Read each question carefully, and answer each question completely. Show all of your work. No credit will be given for unsupported answers. Write your solutions clearly and legibly. No credit will be given for illegible solutions. 1. (6 points) The function E ( x ) is deﬁned by E ( x ) = 1 2 + 1 2 π Z x 0 e - t 2 2 dt . (a) Compute E (0). (b) Compute E 0 (0). (c) Compute E 0 (1). # Score 1 2 3 4 5 6 7 8 9 Σ

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2. (8 points) Compute the following deﬁnite integrals. (a) Z 1 0 xe x 2 dx (b) Z 1 0 x 3 e x 2 dx
3. (4 points) Use the Trapezoidal Rule with four subintervals ( n = 4) to estimate Z 4 0 1 1 + x 3 dx . Do not simplify the resulting expression. 4. (4 points) Determine whether Z 1 x - 5 2 dx converges, and if it does, ﬁnd its value.

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5. (4 points) After conducting extensive research, the American Automobile Association has discovered that the length of time between tuneups for minivans is a continuous random variable T , measured in years, and that the probability density function for T is f ( T ) = ± 0 if T < 0 1 9 Te - T 3 if T 0 What is the probability that a minivan will be driven between one and two years

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Unformatted text preview: between tuneups? 6. (6 points) The mass of a sample of Polonium-210 decreases at a rate proportional to its mass. Let P ( t ) denote the mass of a sample of Polonium-210 at time t , with t measured in days. (a) Write a diﬀerential equation for P ( t ). (b) Solve the diﬀerential equation for P ( t ). (c) If P (0) = 50 grams and P (72 days) = 35 grams, ﬁnd P (100 days). 7. (6 points) Consider the diﬀerential equation y = 4-y 2 . (a) What are the equilibrium (constant) solutions? (b) For what values of y is y increasing? (c) For what values of y is y decreasing? 8. (4 points) Find the area of the region enclosed by the curves y = x 2-4 x and y = 2 x-x 2 . 9. (4 points) Find the volume of the solid obtained by rotating the region enclosed by the graph of y = p sin(3 x ) and the x-axis from x = 0 to x = π 3 about the x-axis....
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final_wi04 - between tuneups 6(6 points The mass of a...

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