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Chapter 12: Q. 13 (page 989)

Find the set of points where the function is continuous.

f(x,y)=x+yx-y

Short Answer

Expert verified

f(x,y)=x+yx-yiscontinuousforall(x,y)in鈩�2exceptwhenx=y.

Step by step solution

01

Step 1. Given information is:

f(x,y)=x+yx-y

02

Step 2. Finding Points

Givenfunctionisrationalfunctionwithdenominatorx-y.Sof(x,y)iscontinuousatallpoints(x,y)in鈩�2exceptatthosepointswherex-y=0Since,x-y=0ifx=yTherefore,f(x,y)=x+yx-yiscontinuousforall(x,y)in鈩�2exceptwhenx=y.

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Most popular questions from this chapter

In Exercises 24鈥�32, find the maximum and minimum of the functionf subject to the given constraint. In each case explain why the maximum and minimum must both exist.

f(x,y,z)=xyzwhenx2+4y2+16z2=64

Describe the meanings of each of the following mathematical expressions :

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

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