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Chapter 12: Q. 14 (page 989)

Find the set of points where the function is continuous.

f(x,y)=x+yx2+y2

Short Answer

Expert verified

f(x,y)=x+yx2+y2iscontinuousforall(x,y)inℝ2exceptat(0,0).

Step by step solution

01

Step 1. Given information is: 

f(x,y)=x+yx2+y2

02

Step 2. Finding Points

Givenfunctionisrationalfunctionwithdenominatorx2+y2.Sof(x,y)iscontinuousatallpoints(x,y)inℝ2exceptatthosepointswherex2+y2=0Since,x2+y2=0ifx=y=0Therefore,f(x,y)=x+yx2+y2iscontinuousforall(x,y)inℝ2exceptat(0,0).

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Most popular questions from this chapter

Find the gradient of the given function, and find the direction in which the function increases most rapidly at the specified point P.

f(x,y)=xsin⁡y,P=3,π2

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