The following question is free response. You will not respond to it in Canvas. Please write your answers down on paper. You will submit your hand-written free response answer in Crowdmark. You must show full detailed work for credit on this.

Compute the left Riemann sum, using four subintervals (that is, ), for on the interval

(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

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

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

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)