Note: please write down the Answer by hand on paper and also write each answer with the number of the questions

MATH 209: calculus 3

1. Use linear approximation to evaluate V (4.02)2 + (3.99) 2 + (2.03) 2.2. Find the equation of the tangent plane to the given surface at the specified point. 2 = xezy, (2,0,2)3. Compute the directional derivative of the hemisphere z = val -x2 - y at the point a a a in the direction making an angle 7/4 with the positive x-axis. V3' V3' V34. (a) Find the directional derivative of f(x, y) = 4 -x2 - Ty at (1,2) in the direction of d = cos(7 / 3)2 + sin(7 /3)3. (b) Find the directional derivative of f(x, y) = x2 sin 2y at (1, 7/2) in the direction of u = 32 -4j