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Chapter 12: Q 21. (page 916)

In Exercise, provide a rough sketch of the graph of a function of two variables with the specified level “curve(s).”

All of the level curves are squares.

Short Answer

Expert verified

All of the level curves are squares.

Step by step solution

01

Step 1. Given information

All of the level curves are squares.

02

Step 2. Explanation

The goal is to create a crude graph of a function of two variables with "all of the level curves are squares."

The graph must have a single point at a value of $z$ to have a single point as one of the level curves.

A square pyramid is an example of this.

The following is an example of a rough sketch.

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Most popular questions from this chapter

Construct examples of the thing(s) described in

the following.

Try to find examples that are different than

any in the reading.

(a) A function z = f(x, y) for which ∇f(0, 0) = 0 but f is

not differentiable at (0, 0).

(b) A function z = f(x, y) for which ∇f(0, 0) = 0 for every

point in R2.

(c) A function z = f(x, y) and a unit vector u such that

Du f(0, 0) = ∇f(0, 0) · u.

Describe the meanings of each of the following mathematical expressions:

fzx0,y0,z0

Describe the meanings of each of the following mathematical expressions

∂w∂x

Use Theorem 12.32 to find the indicated derivatives in Exercises 21–26. Express your answers as functions of a single variable.

dzdtwhenz=x3ey,x=sint,andy=cost

In Exercises 21–26, find the discriminant of the given function.

gx,y=e-3xsin2y.
See all solutions

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