## Math 122 Study Guide: Exam 8 (13.1 - 13.5)

1. Identify the curve by transforming to rectangular coordinates. Two parts.
2. Express the equations in polar coordinates. Two parts.
3. Find the area of the polar region described.
4. Sketch the curve in polar coordinates and give its name. Six parts.
5. Sketch the curve by eliminating the parameter t, and indicate the direction of increasing t. Three parts.
6. Find the arc length of the curve in parametric form.
7. Find the arc length of the curve in polar form.
8. Find dy/dx for a parametric equation.
9. Find the second derivative of y wrt x, without eliminating the parameter, for a specific value of the parameter.
10. Find the slope of the tangent to the curve at the point with the given value of theta.

### Notes

• No Calculators
• All problems are directly from the text.
• You may use note cards.
• The note cards may contain
• The formulas for converting between polar and rectangular coordinates
• The symmetry tests for polar coordinates
• The equations for lines, circles, cardiods, limacons, lemniscates, spirals, roses, and conic sections with an accompanying graph. The equations must be the generic ones with a's and b's, not specific values.
• The formula for the area of a curve in polar coordinates.
• Instructions on finding the second derivative of y with respect to x for a parametrically defined equation.
• The arc length formulas for parametric and polar equations.
• Surface area of revolution for a parametrically defined equation.
• The unit circle with values of sin x and cos x. You really ought to have this one memorized.