final_wi03

final_wi03 - checkup(b What is the probability that a...

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Name: Section: TA: Time: Math 10B. Final Examination March 18, 2003 Read each question carefully, and answer each question completely. Show all algebraic steps; no credit will be given for unsupported answers. 1. The Fresnel Sine Function S( x ) is defined by S( x ) = x 0 sin π 2 t 2 dt . (a) Compute S(0). (b) Compute S (0). (c) Compute S (1). # Score 1 2 3 4 5 6 7 8 9 Σ

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2. Compute 3 - 3 9 - x 2 dx . 3. Compute the following definite integrals. (a) π 2 0 x cos ( x 2 ) dx (b) π 2 0 x 3 cos ( x 2 ) dx
4. Use the Midpoint Rule with two subintervals ( n = 2) to estimate 2 0 1 1 + x 3 dx . Do not simplify the resulting expression. 5. Determine whether 1 1 x dx converges, and if it does, find its value.

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6. After conducting extensive research, the American Dental Association has discovered that the length of time between dental checkups for dental patients is a random variable T , measured in years, and that the probability density function for T is f ( T ) = 0 if T < 0 1 4 Te - T 2 if T 0 (a) What is the probability that a dental patient will wait less than a year for a dental

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Unformatted text preview: checkup? (b) What is the probability that a dental patient will wait between two and three years for a dental checkup? 7. Consider the diﬀerential equation y = 2 y (1-y ). (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. Find the area of the region enclosed by the curves y = 4-x 2 and y = 4 x (2-x ) and between x = 0 and x = 2. 9. 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) = 100 grams and P (140 days) = 50 grams, ﬁnd P (200 days)....
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