calculate the limit if it exists and justify your response if it does not exist

Question

calculate the limit if it exists and justify your response if it does not exist 1)lim(x,y)->(00) x-y+2square root x-2square root y/square root x-square root y 2)lim(x,y,z)->(-1/4,pi/2,2) arctan(xyz) 3)lim(x,y)->(0,0)xy/IxyI 4)lim(x,y)->(1,1) xy^2-1/y-1

Explanation / Answer

1. lim(x,y)->(00) x-y+2square root x-2square root y/square root x-square root y = does not exit , because left hand limit not exit 2. lim(x,y,z)->(-1/4,pi/2,2) arctan(xyz) = -1 3.lim(x,y)->(0,0) xy/IxyI = 1 4)lim(x,y)->(1,1) xy^2-1/y-1 not exit , because function is infinity at y=1

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