Asg3 - M miles toward the coast is M x f dx T ) ( 15 Use...

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MATH 118 – Spring 2010 Assignment 3 Due: Thursday, May 27 1. Textbook, Page 526, Exercises 8.6, # 7, 11, 21. 2. Textbook, Page 537, Exercises 8.7, # 9, 17, 21. 3. When two chemicals A and B are combined a compound C is formed. The resulting second-order reaction between the two chemicals is modeled by the differential equation ) 40 )( 250 ( X X k dt dX where ) ( t X denotes the number of grams of the compound C present at time t . Determine ) ( t X if it is known that 0 ) 0 ( X (g) and 30 ) 10 ( X (g). 4. Scientists estimate the arrival times of tsunamis (seismic ocean waves) based on the point of origin P and ocean depths. The speed of a tsunami in miles per hour is approximately d 15 , where d is the ocean depth in feet. Let ) ( x f be the ocean depth x miles from P (in the direction of the coast). The time T required for the tsunami to travel
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Unformatted text preview: M miles toward the coast is M x f dx T ) ( 15 Use Simpson's rule to estimate T if 1000 M and the ocean depth (in feet), measured at 100-mile intervals starting from P , are 13000, 11500, 10500, 9000, 8500, 7000, 6000, 4400, 3800, 3200, 2000 5. When approximating the definite integral 3 / 1 2 dx e x by using (a) the trapezoidal rule, (b) the Simpsons rule, give for each case the number of subdivisions of the interval of integration that is required to guarantee an error of less that 10 4 . (It is not necessary to approximate the value of this definite integral). Recommended Problems (NOT to be handed in) Textbook, Page 526, Exercises 8.6, # 2-26 (even), 30, 36, 38. Textbook, Page 537, Exercises 8.7, # 2-14 (even), 20, 22....
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