Question

if z = 5x2 y2 and (x, y) changes from (1, 1) to (0.95, 0.9), compare the values of δz and dz. (round your answers to four decimal places.)

Answer 1

To compare the values of δz and dz, we can use the partial derivatives of z with respect to x and y.

Step-by-step explanation:

Given that z = 5x^2y^2, the change in z, denoted as δz, can be calculated using the formula δz = dz/dx × δx + dz/dy × δy.

To find dz, we can differentiate z with respect to x and y. Taking the partial derivative with respect to x, we get dz/dx = 10xy^2. Taking the partial derivative with respect to y, we get dz/dy = 10x^2y.

Substituting the given values of (x, y) as (1, 1) and (0.95, 0.9), we can calculate the values of δz and dz. The values of δz and dz will depend on the values of δx and δy.