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Chapter 12: Q. 17 (page 989)

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

f(x,y,z)=x+y+zx鈭�2y+3z

Short Answer

Expert verified

The given function is continuous for all (x, y, z) inR3at all points except those where x-2y+3z=0

Step by step solution

01

Step 1. Given information

f(x,y,z)=x+y+zx鈭�2y+3z

02

Step 2. Explanation

The given function f(x,y,z)=x+y+zx鈭�2y+3zis a rational function.

Therefore, f(x, y, z) is continuous for all (x, y, z) in R3at all points except those where x-2y+3z=0

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Most popular questions from this chapter

In Exercises, find the maximum and minimum of the function f subject to the given constraint. In each case explain why the maximum and minimum must both exist.

f(x,y,z)=x+y+zwhenx2+4y2+16z2=64

Evaluate the following limits, or explain why the limit does not exist.

lim(x,y)鈫�(0,0)x3+y3x2+y2

Letf(x)beadifferentiablefunctionofx,g(y)beadifferentiablefunctionofy,andh(x,y)=f(x)+g(y).Provethat鈭�2h鈭�x鈭�y=鈭�2h鈭�y鈭�x.

Use Theorem 12.33 to find the indicated derivatives in Exercises 27鈥�30. Express your answers as functions of two variables.

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

drdtwhenr=x2+y2,x=tandy=t2
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