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Chapter 12: Q. 18 (page 989)

Continuity: Find the set of points where the function is continuous.

f(x,y,z)=x+y+zx2+y2+z2

Short Answer

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Step by step solution

01

Step 1. Given information

f(x,y,z)=x+y+zx2+y2+z2

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Most popular questions from this chapter

In Exercises, by considering the function f(x,y)=x2ysubject to the constraint x+y=0,you will explore a situation in which the method of Lagrange multipliers does not provide an extremum of a function.

Show that the only point given by the method of Lagrange multipliers for the function f(x,y)=x2ysubject to the constraint x+y=0is(0,0).

Describe the meanings of each of the following mathematical expressions:

∇f(x,y)

In Exercises 37-42, use the partial derivatives of gx,y=xcosyand the point 1,πspecified to

afind the equation of the line tangent to the surface defined by the function in the xdirection,

bfind the equation of the line tangent to the surface defined by the function in the ydirection, and

cfind the equation of the plane containing the lines you found in parts aand b.

Describe the meanings of each of the following mathematical expressions:

fzx0,y0,z0

Use Theorem 12.32 to find the indicated derivatives in Exercises 21–26. Express your answers as functions of a single variable. dxdtwhenx=rcosθ,r=t2−5,andθ=t3+1
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