Set up an integral to find the surface area by revolving the parametric curve with equations

This is a matching exercise. Match the equation of each curve to the correct arc length integral. Find the arc length for each of the following curves, in xy, parametric, and polar coordinates. Equation 1 (xy) Equation 2 (parametric) Equation 3 (polar)

Which of the following is correctly matched with its type and use?

Which of the following techniques directly counts individual bacterial cells?

A researcher uses a spectrophotometer to monitor bacterial growth.  Which limitation applies?

A food processor finds bacterial contamination in products stored at 40 C .  What category of bacteria is likely growing?    

Which test evaluates the effectiveness of disinfectants on actual surfaces under normal use?

A disinfectant passes the use-dilution test but fails the in-use test.  What does this suggest?

You count colonies after serial dilution and plating.  Why is this method useful?  

In which phase is the bacterial population doubling at a constant rate?