Question

Using total differentials, find the approximate change of the given function when x changes from 0 to 0.37 and y changes from 0 to 0.31. If necessary, round your answer to fo.

Answer 1

To find the approximate change of a given function using total differentials, we need to find the partial derivatives and substitute the given values for dx and dy. In this case, since the function y = 0.011 does not depend on x, the change in y will be approximately equal to ∂y/∂y * dy, which is 0.31.

Step-by-step explanation:

To find the approximate change of a given function using total differentials, we can use the formula:

dF = ∂F/∂x * dx + ∂F/∂y * dy

Here, ∂F/∂x and ∂F/∂y are the partial derivatives of the function F with respect to x and y, and dx and dy are the changes in x and y respectively.

In this case, since we are given the function y = 0.011, we need to find the partial derivatives ∂y/∂x and ∂y/∂y and substitute the given values for dx and dy.

Since the function y = 0.011 does not depend on x, ∂y/∂x = 0. Thus, the change in y will be approximately equal to ∂y/∂y * dy.

Substituting the given values: ∂y/∂y = 1, dy = 0.31 - 0 = 0.31.

Therefore, the approximate change in y is 1 * 0.31 = 0.31.