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Consider the function f(x

Question

Consider the function f(x,

y) = 2x p x 2 + y 2 , (x, y) 6= (0, 0). (a) (4 points) Find lim (x,y)→(0,0) f(x, y) along the path y = x for x 0 or show that the limit does not exist. (b) (4 points) Find lim (x,y)→(0,0) f(x, y) along the path y = 2x for x 0 or show that the limit does not exist. (c) (2 points) Find lim (x,y)→(0,0) f(x, y) or show that the limit does not exist.

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Question 3. Consider the function f(x, y) =
VI2 + y2
(x, y) # (0,0).
(a) (4 points) Find lim f(x, y) along the path y = x for a gt; 0 or show that the limit
does not exist.
(z,3)-+(0,0)
(b) (4 points) Find lim f(x, y) along the path y = 2x for r gt; 0 or show that the limit
does not exist.
(2,y) +(0,0)
(c) (2 points) Find lim f(r, y) or show that the limit does not exist.
+
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Consider the function f(x