Find

Use an appropriate trigonometric substitution to convert the following integral into a trigonometric integral in terms of Simplify the integral as much as possible, but do not integrate it.

Find

Find

Either evaluate or show that it diverges.

Use the Integral Test to determine if converges or diverges.

Let

1. Find all points on the curve where the tangent line is either horizontal or vertical.
   
   
   
   

2. Use an analysis of the intervals in which the curve rises and falls (as discussed in class) to sketch the curve on the axes below. Indicate with arrows the direction in which the curve is traced as increases.
   
   

Convert each point given in polar coordinates into rectangular coordinates.