Solved: Approximate function change Use differentials to

Chapter 10, Problem 30E

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QUESTION:

Approximate function change Use differentials to approximate the change in z for the given changes in the independent variables.

z = In (1 + x + y) when (x, y) changes from (0,0) to (-0.1, 0.03)

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QUESTION:

Approximate function change Use differentials to approximate the change in z for the given changes in the independent variables.

z = In (1 + x + y) when (x, y) changes from (0,0) to (-0.1, 0.03)

ANSWER:

Solution 30E

Step 1 of 3:

In this problem we need to use differentials to approximate the change in z for the given changes in the independent variables.

Let  be differentiable at the point . The change in as the independent variables change from to is denoted and is approximated by the differential :

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