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Evaluate: ("lim")(x→0,y→0)(y^2+sinx)/(x^...

Evaluate: `("lim")_(x→0,y→0)(y^2+sinx)/(x^2+siny^2)` where `(x , y)→(0,0)` along the curve `x=y^2`

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The correct Answer is:
2
`underset(yto0)underset(xto0)lim(y^(2)+sin x)/(x^(2)+siny^(2))=underset(xto0)lim(x+sinx)/(x^(2)+sinx)=underset(xto0)lim(1+(sinx)/(x))/(x+(sinx)/(x))=2`
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