We've climbed many mathematical mountains this semester, so here's a sweet final problem to wrap things up! The top half of the infamous "Mount Donut" is modeled by the surface z = f(x, y), where f(x, y) = 19 -(Vx2+ 2 - 4)? A. [10 pts] Find the domain and range of f(x, y), and sketch the domain on the graph below. Make sure to simplify your final answers and show your work. y 7-6-5-4-3-2-1 1 1 2 3 4 5 6 7B. [5 pts] Calculate fr(x, y). If you do it carefully, you should find that Va2 + y2 - 4 fx(x, y) = - 2 Vx2 + y2 . 1/9 - (v x2 + y2 - 4Analogously, fy (27, y) = . You may use this formula for the rest of this problem. Now, suppose that there is a donut shop at the point {4, U, 3) on the surface. Jim starts at the point [7, U, U) and bikes up the surface above the :r-direction in the Iy-plane. A vector-valued function that traces his position in time is given by I:0?) = (Lam/W), which is valid from t = U until the time Jim rst reaches the donut shop. The rest of the parts of this problem refer to the curve parameterized by the vector-valued function above. C. [10 pts] Set up an integral that gives the distance Jim travels during his hike. Then, evaluate the integral by using technology and give the distance Jim travels to 1 decimal place. Make sure to state What you used to evaluate the integral. D. [10 pts] Show that Vf(5, 0) is orthogonal to the level curve of f(r, y) through (5, 0). Hint: A parameterization for this level curve should be part of your solution