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Question Number 197008 by tri26112004 last updated on 06/Sep/23

Answered by MM42 last updated on 07/Sep/23

a) if x=y⇒lim_((x,y)→(0,0)) ((x^2 −y^2 )/(x^2 +y^2 )) =0 if y=2x⇒lim_((x,y)→(0,0)) ((x^2 −y^2 )/(x^2 +y^2 )) =lim_(x→0) ((−3x^2 )/(5x^2 ))=−(3/5) ⇒ lim “ not exist ” ✓ b) lim_((x,y)→(0,2)) ((x^2 +(y−2)^2 )/((x^2 +(y−2)^2 )((√(x^2 +(y−2)^2 +1))+1))) =(1/2) ✓

a)ifx=y⇒lim(x,y)→(0,0)x2−y2x2+y2=0ify=2x⇒lim(x,y)→(0,0)x2−y2x2+y2=limx→0−3x25x2=−35⇒lim‘‘notexist″✓b)lim(x,y)→(0,2)x2+(y−2)2(x2+(y−2)2)(x2+(y−2)2+1+1)=12✓

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