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(A): If then compute =[A]   (B): If then compute [B] (C): If then compute [C]

Free Response (16 points) Use the following definition to evaluate the integral

The area of the region enclosed by the graph of  and the line  is

(A): if then compute =[A].   (B): if then compute [B].   (C): if . Then compute [C].

A bacteria colony is cultivated in a laboratory. The number of bacteria increases at a rate of  hundred strands per day (t is time in days). Find the increase in bacteria population after 4 days, assuming that there are 1 hundred strands of bacteria at time t=0.

Find the power series representation centered at 0 for  

Find the power series representation centered at 0 for

Calculate the volume of the figure whose base is a unit circle, and whose cross sections perpendicular to the y-axis are squares.  (enter the lowest fraction form, for example 7/24)

Determin the radius (R) and the interval of convergence (IOC) of the power series

Calculate the volume of the figure whose base is a unit circle, and whose cross sections perpendicular to the x-axis are squares.  (enter the lowest fraction form, for example 7/24)