Question1 Bounding the Error in Linear Approximations In Exercises 33-38, find the linearization L(x, y) of the function f(x, y) at Po. Then find an upper bound for the magnitude E of the error in the approximation f(x, y) ~ L(x, y) over the rectangle R. 33. f(x, y) = x2 - 3xy + 5 at Po(2, 1), R: |x - 2| $ 0.1, |y - 1 = 0.1 34. f(x, y) = (1/2)x2 + xy + (1/4 )y2 + 3x - 3y + 4 at Po(2, 2), R: |x - 2 5 0.1, |y - 2 5 0.1 35. f(x, y) = 1 + y + xcosy at Po(0, 0), R: |x) = 0.2, ly) = 0.2 (Use | cos y) $ 1 and | sin y) $ 1 in estimating E.) 36. f(x, y) = xy2 + y cos (x - 1) at Po(1, 2), R: |x - 1 0.1, ly - 2 5 0.1 37. f(x, y) = e" cosy at Po(0, 0), R: |x 5 0.1, y S 0.1 (Use e - 1.1 1 and |cos y) = 1 in estimating E.) 38. f(x, y) = Inx + Iny at Po(1, 1), R: |x - 1| = 0.2, |y - 1| = 0.2 .jpg