Does \lim_{(x,y)\to(3,-1)}\frac{(x-3)(y+1)}{(x-3)^2+(y+1)^2} exist?

Carol Gates 2021-10-25 Answered
Does lim(x,y)(3,1)(x3)(y+1)(x3)2+(y+1)2 exist?
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Expert Answer

jlo2niT
Answered 2021-10-26 Author has 96 answers
Given that lim(x,y)(3,1)(x3)(y+1)(x3)2+(y+1)2
The value of the limit lim(x,y)(3,1)(x3)(y+1)(x3)2+(y+1)2 do not exist as the denominator becomes 0.
Evaluate lim(x,y)(3,1)(x3)(y+1)(x3)2+(y+1)2 as shown below
lim(x,y)(3,1)(x3)(y+1)(x3)2+(y+1)2=(03)(0+1)(03)2+(0+1)2
=(3)(1)9+1
=310
Therefore, the limits when x=0 and y=0 lim(x,y)(3,1)(x3)(y+1)(x3)2+(y+1)2=310.
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