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Chapter 12: Q. 9 (page 989)

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

lim(x,y,z)鈫�(1,0,-1)sin(xy)x2-y2+z2

Short Answer

Expert verified

lim(x,y,z)鈫�(1,0,-1)sin(xy)x2-y2+z2=0

Step by step solution

01

Step 1. Given information is:

lim(x,y,z)鈫�(1,0,-1)sin(xy)x2-y2+z2

02

Step 2. Evaluating Limits 

Since,(x,y,z)鈫�(1,0,-1)sin(xy)鈫�0andx2-y2+z2鈫�2whichisfiniteSothefunctionsin(xy)x2-y2+z2iscontinuousat(1,0,-1).So,lim(x,y,z)鈫�(1,0,-1)sin(xy)x2-y2+z2=sin(0)12-02+(-1)2=0Hence,lim(x,y,z)鈫�(1,0,-1)sin(xy)x2-y2+z2=0

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