# Study Guide - Final 1

## Math 221

1. Given three points P,Q, and R, find the vectors u=PQ and v=PR and then u dot v and u cross v.
2. Find the equation of the plane passing through the given point orthogonal to the given line (in symmetric form).
3. Find the equation of the line (in parametric form) passing through the given point and parallel to the given vector.
4. Given a space curve, find r', r", Dt ||r||, and the equation of the line tangent to the curve at a given point.
5. Find all second partial derivatives Fxx, Fxy, Fyx, and Fyy, and verify that the second mixed partials Fxy and Fyx are equal.
6. Evaluate the double and triple integrals.
7. Use a multiple integral and a convenient coordinate system to find the volume of the solid bounded by the graphs of the given equations.
8. Determine if a vector field is conservative. If it is, find the potential function.
9. Find the divergence and curl of a vector field.
10. Evaluate a line integral: int F dot dr.
11. Find the general solution to a first-order separable differential equation.
12. Find the particular solution of the second-order homogeneous linear differential equation that satisfies the initial conditions.

Hint. You really ought to know the derivatives of the three inverse trig functions should one of them appear in an antiderivative somewhere along about problem 11.