Evaluate the following limits. lim_{(x,y)rightarrow(1,-2)}frac{y^2+2xy}{y+2x}

Question
Limits and continuity
Evaluate the following limits. $$\lim_{(x,y)\rightarrow(1,-2)}\frac{y^2+2xy}{y+2x}$$

2021-03-05
The given expression $$\lim_{(x,y)\rightarrow(1,-2)}\frac{y^2+2xy}{y+2x}$$
Calculation
$$\lim_{(x,y)\rightarrow(1,-2)}\frac{y^2+2xy}{y+2x}=\lim_{(x,y)\rightarrow(1,-2)}\frac{y(y+2x)}{y+2x}$$
$$=\lim_{(x,y)\rightarrow(1,-2)}$$
$$=-2$$

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