Question
Find the limit, if it exists, or show that the limit does not exist.$ \displaystyle \lim_{(x, y) \to (1, 0)} \dfrac{xy - y}{(x - 1)^2 + y^2} $
Step 1
Substituting $y=0$ into the function, we get \[f(x,0) = \dfrac{x(0) - 0}{(x - 1)^2 + 0^2} = 0\] So, as $(x, y) \to (1, 0)$ along the line $y=0$, $f(x,y) \to 0$. Show more…
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