find the linearization L(x,y) of the function f(x,y) at the point 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. f(x,y)=(xy^2)+(ycos(x-1)) at Po(1,2) R: |x-1|

Question

find the linearization L(x,y) of the function f(x,y) at the point 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.                     f(x,y)=(xy^2)+(ycos(x-1))     at Po(1,2)                     R: |x-1| <= 0.1   ,       |y-2|<=0.1

amistre64 · Answer

to flatten a curve, we make a line; to flatten a surface we create a plane

amistre64 · Answer

ideally, we can generate a suitable plane equation with partial derivatives that mirrors the point slope form of a line.
$$z = F_x(x-x_o)+F_y(y-y_o)+z_o$$