1. Sketch a contour map of the surface using level curves for the given c-values. 2 = x'+417, c= 0, 1,2,3,4 2. (a) Find both first partial derivatives. i. f (x, y ) = e (* ly? ) ii. z = In - cty T - y iii. z = cos (b) Evaluate fr, fy, and fz at the given point. i. f (r, y, = ) = yz (1, -1, -1) ii. f (x, y, z) = zsin (x + y) , (0, 7, -4) (c) Find the four second partial derivatives. Observe that the second mixed partials are equal. i. z = e tany ii. = = arctan 3. (a) Differentiate implicitly to find 93 as and #5. z = esin(y + 2) (b) Differentiate implicitly to find the tu and du Dz . T y- 2=0