a) Write down the equation of the tangent plane to the graph of the function f(x, y) 2² - xy + y² +3 at the point P = (3,2, 8). (b) Use the linearization of the same fat a nearby point to approximate f(2.97, 2.02). 5. The radii, R and r, and the height h of a truncated circular cone are measured to be 30, 20, and 40 centimeters, with respective errors of 1, 1, and 2 millimeters. Find the error you make by using these values in computing the volume V = (R²+r² + Rr). 6. Determine aw/ar at r = 1 and s= -1, if w = (x+y+z)², x=r-s, y = cos(r + s) and z = sin(r + s). 7. Find the derivative of f(x, y, z) = 2³ xy² - z at Po = (1,1,0) in the direction of v = 2i - 3j+ 6k. What is the direction in which f increases the most rapidly around Po? 8. Find the equations of the tangent plane and normal line to the paraboloid x² + y² + z = 9 at P = (1,2,4).
