# jcksparrwhfdys11y.docx - 1 A particle moves during the...

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1. A particle moves during the interval of time from t = 1 second to t = 3 seconds with a velocity given by v ( t ) = t 2 + 2 t + 1 feet per second. Find the total distance that the particle has moved and also the average velocity. 2. For each of the functions and intervals in Problem ?? , find a number c such that a < c < b and M b ( f ) = 3. An arbitrary linear function f is defined by f ( x ) = Ax + B for some constants A and B . Show that M b ( f ) = f ( a ) + f ( a 2 4. Let x ( t ) be the number of bacteria in a culture at time t , and let 0 = x (0). The number grows at a rate proportional to the number present, and doubles in a time interval of length T . Find an expression for x ( t ) in terms of 0 and T , and find the average number of bacteria present over the time interval [0 , T a f ( c ). b ) . x x ].
8.1 Riemann Sums and the Trapezoid Rule. This section is divided into two parts. The first is devoted to an alternative ap- proach to the definite integral, which is useful for many purposes. The second is an application