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1. Police chase: A speeder traveling 45 miles per hour (in a 25 mph zone) passes a stopped police car which immediately takes off after the speeder. If the police car speeds up steadily to 60 miles/hour in 10 seconds and then travels at a steady 60 miles/hour, how long and how far before the police car catches the speeder who continued traveling at 45 miles/hour?
2. Suppose we divide the interval [ 1, 4] into 100 equally wide subintervals and calculate a Riemann sum for f(x) = 1 + x2 by randomly selecting a point ci in each subinterval. We can be certain that the value of the Riemann sum is within what distance of the exact value of the area between the graph of f and the interval [ 1, 4] ? (b) What if we take 200 equally long subintervals?
