6. (10pts) An object is in motion according to the conditions: a(t ) =, (0) =, and (0) =. Find the velocity and position functions for this motion. What is the maximum height (z value) that this object reaches? 7. (10pts) Let f (x, )) = The domain for this function is all points (x, y) except (0, 0), and it is continuous for all (x, y) in its domain. Can ((x, y) be made continuous at (0, 0) by defining (0, 0) to be a specific value? Explain! Draw the level curves for this function for function values: 0, 0.5, 1. 8. (10pts) Find the partials #% and- : with z defined implicitly as a function of x and y in the equation 3xz - xy + 2z' +3w = 5. 9. (10pts) Suppose that a mountain climber is at the point (500, 300, 3390) on the surface of a mountain described by the function k(x, y) = 4000-0.001x -0.004y. In what direction would the climber have the steepest up slope? What is that slope? 10. (10pts) Find the equation of the plane tangent to the surface z = x' - 3xy + y' at the point P(1, 2, 3) on the surface