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- 1.
- Consider the function
*f*(*x*) =*x*-6^{3}*x*+5^{2}*x*+12 on the interval [-1,3]. Use the command`leftsum`to approximate the definite integral to two decimal places. Then explain why the`leftsum`and`rightsum`commands give the same numerical values for the same number of subintervals. (Hint - use the`leftbox`and`rightbox`commands to see what is going on.) - 2.
- Suppose that the velocity of a particle moving in one dimension
is given by
Find the average value of
*v*(*t*) on the following time intervals.- (a)
- [0,3]
- (b)
- [0,6]
- (c)
- [3,6]

- 3.
- Let the continuous function
*v*(*t*) represent the velocity of a particle moving in one dimension. Let*a*and*b*be real numbers in the domain of*v*and let*c*be (*a*+*b*)/2. That is,*c*is exactly halfway between*a*and*b*. Show that the following equation is always satisfied where is the average value of*v*on the interval [*a*,*b*], is the average value of*v*on the interval [*a*,*c*], and is the average value of*v*on the interval [*c*.*b*]. Note - this is not a Maple problem. This problem is a thinking problem. I would suggest leaving some space on your worksheet and writing your answer in by hand. Part of using Maple is learning when not to use it.

1/16/1998