数学题在线解答

问题:求极限lim√(x^2+y^2)-x/y^2

结论/结果
1/2
解答

\begin{aligned}
& \lim_{(x,y)\rightarrow (1,0)}\frac{\sqrt{x^2+y^2}-x}{y^2}\\
=& \lim_{(x,y)\rightarrow (1,0)}\frac{x^2+y^2-x^2}{y^2\cdot(\sqrt{x^2+y^2}+x)}\\
=& \lim_{(x,y)\rightarrow (1,0)}\frac{1}{\sqrt{x^2+y^2}+x}\\
=& \frac{1}{\sqrt{1^2+0^2}+1}\\
=& \frac{1}{2}
\end{aligned}

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