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Chapter 12: Q. 11 (page 989)

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

lim(x,y)鈫�(0,0)x=0x2+y2x2-y2

Short Answer

Expert verified

lim(x,y)鈫�(0,0)x=0x2+y2x2-y2=-1

Step by step solution

01

Step 1. Given information is:

lim(x,y)鈫�(0,0)x=0x2+y2x2-y2

02

Step 2. Evaluating Limits 

Asthegivenlimitlim(x,y)鈫�(0,0)x=0x2+y2x2-y2hastobeevaluatedalonthelinex=0,solim(x,y)鈫�(0,0)x=0x2+y2x2-y2=limy鈫�002+y202-y2lim(x,y)鈫�(0,0)x=0x2+y2x2-y2=limy鈫�0(-1)lim(x,y)鈫�(0,0)x=0x2+y2x2-y2=-1Therefore,lim(x,y)鈫�(0,0)x=0x2+y2x2-y2=-1

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