Author: Anonymous

Let R be the region bounded by the graph of  and the y-axis. The region R is the base of a solid. For this solid, the cross sections perpendicular to the y-axis are rectangles with height equal to six times the length of their base. Find the volume of the solid. Approximate to the nearest thousandths place.

Find the position for a particle with acceleration   Given the initial conditions

Find the area under a curve defined with the parametric equations  from x = 0 to x = 9.

Let R be the region bounded by the graph of   and the lines and . The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are semicircles. Find the volume of the solid. Approximate to the nearest thousandths place.

Consider the sequence . Does  converge or diverge? If the sequence converges, give its limit as a decimal. Otherwise select “diverges”.

A particle’s acceleration is given by . If , find the particle’s speed at time .

True or False:  is monotonic and bounded and therefore convergent.

A slope field is displayed on a coordinate grid from approximately negative seven to seven on both axes. The short line segments form vertical bands in which the slope is the same for all y-values at a given x-value. At regularly spaced x-values, the segments are horizontal, indicating slope equals zero along those vertical lines. Moving left or right across the graph, the slopes oscillate in a repeating pattern: negative, zero, positive, zero, and negative again. The steepness increases between the zero-slope lines before flattening again at the next vertical band. The slope field shown above is for which differential equation?

Approximate the sum of the series  to 4 decimal places. 

Find the volume of the solid generated by revolving the region bounded by the graphs of  and   about the x-axis.