limy→0limx→0y−xy+x⋅1+x21+y2=limy→01⋅11+y2=1\lim_{y\rightarrow0} \lim_{x\rightarrow0} \dfrac {y-x} {y+x}\cdot \dfrac {1+x^2}{1+y^2}= \lim_{y\rightarrow0} 1\cdot \dfrac {1}{1+y^2}=1limy→0limx→0y+xy−x⋅1+y21+x2=limy→01⋅1+y21=1
limx→0limy→0y−xy+x⋅1+x21+y2=limx→0−1⋅1+x21=−1\lim_{x\rightarrow0} \lim_{y\rightarrow0} \dfrac {y-x} {y+x}\cdot \dfrac {1+x^2}{1+y^2}= \lim_{x\rightarrow0} -1\cdot \dfrac {1+x^2}{1}=-1limx→0limy→0y+xy−x⋅1+y21+x2=limx→0−1⋅11+x2=−1
The repeated limits don`t coincide so the simultaneous limit doesn`t exist
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