Consider the function 𝑓(𝑥, 𝑦) = 𝑥𝑦 ( 𝑥 2−𝑦 2 𝑥 2+𝑦2 ) , (𝑥, 𝑦) ≠ (0, 0). Show that lim (𝑥,𝑦)→(0,0) 𝑓(𝑥, 𝑦) = 0
"lim_{(\ud835\udc65,\ud835\udc66)\u2192(0,0)} \ud835\udc53(\ud835\udc65, \ud835\udc66)\\\\\n=lim_{(\ud835\udc65,\ud835\udc66)\u2192(0,0)} \ud835\udc65\ud835\udc66 ( \ud835\udc65^2\u2212\ud835\udc66^2 \ud835\udc65^2+\ud835\udc66^2 )\\\\\n\\text{ put y=mx},\\\\\n=lim_{x\u21920} mx^2 ( \ud835\udc65^2\u2212m^2 \ud835\udc65^4+m^2x^2 )\\\\\n=0"
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