Chapter 16.1, Problem 31E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Match the functions *f* with the plots of their gradient vector fields labeled I-IV. Give reasons for your choices.

**31.** *f*(*x*, *y*) = (*x + y*)^{2}

To determine

**To match:** The function

Explanation

**Given data:**

**Formula used:**

Write the expression for gradient vector field of a two dimensional vector.

Write the required differentiation formulae with respect to

Write the required differentiation formulae with respect to

Rearrange equation (1) as follows.

Differentiate the term

Differentiate the term

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