1. Evaluate lim [(x^2 + y^2)/[(x^2 + y^2 +1)^1/2 -1] (x,y)→(0,0) 2. Evaluate lim [e^(1/x) + arctan(1/y)] (x,y)→(0,0) 这题我把x跟y拆开算, 出现 lim e^(1/x) X lim arctan(1/y) x→0 y→0 然後就不知道该怎麽继续下去了...... 3. Show that lim x/[(x^2 + y^2)^1/2] doesn't exist. (x,y)→(0,0) 这题我用极座标下去做, 最後得到一个 cosψ 然後我写 cosψ 随ψ变化, 所以极限不存在 不知道还需不需要补充什麽? 4. The function f(x,y) = (sin(xy))/xy is defined for xy≠0 Q: Is it possible to extend the domain of f(x,y) to all of R^2 so that the result is a continuous function? Why? 补充一个小问题, L'Hopital's Rule 可以用在多变数极限吗? 以上这些, 就劳烦各位了, 谢谢^^ --

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