MATH 265: MULTIVARIABLE CALCULUS: LESSON 1!) PROBLEMS Problems are worth 2!} points each. (1) Let ee) = \"my. (3} Calculate thm y] . (h) HT; 2 g? -. 33*, nd 133.1(2, E}. [2) Let gfm, y, 2:) = emy +- zlny. Calculate the gradient of g. [3) Use the methods of this section to nd an equation for the plane tangent to the surface dened by the equation 33y + 32 -- 4 = l} at the point (1, 1, 1). (4) Let res} = w? +3.: and let em = {saw}. (a) Compute %f{?[t]) using the Chain Rule {h} Compute TtD without using the Chain Rule, but instead rst writing the composition 31796)) as a function of t, then di'erentiating with respect to t in the usual Cole I way. [Of course, the two answers must be same!) [5) The temperature at the point [I,y, z} in space is given by T{1:, y, z} = a: 1- yz. A y is at the point (I, 2, I]. In what direction should he begin to y to one] o as quieldj,r as possible? Your answer should he a unit vector in the requested direction. (If!) {Bonus question: worth lil points. Total points for assignment exit to exceed 1%.} Suppose a tub has the shape of an elliptical parahuloirl given by z = (1.12 -+ try2 {where o,b are some positive constants). If a marble were released at the point {1, 1,151 + b} on the inside surface of the tub, in what direction wmd it begin to roll? Your answer should be a unit vector in the requested direction