Question

use total differential to approximate the change in z= xy^2 from its value at (0.5 ,1) to its value at (0.503,1.004)compare the magnitude of the error in this approximation with the distance between the points (0.5,1) and (0.503,1.004)​

Answer 1

Concept Used : Directional Derivative

dz/ds|(0.5,1) = (dz/dx).(x-0.5) + (dz/dy).(y-1)

Find ds value as distance between both points and multiply it in RHS. From here you will get dz value ; which is approximate of distance between them.