3. Let x² – y? x2 + y2 - f(x, y) Determine the limit of f(x, y) as (x, y) approaches (0,0) along the curve C. (a) C:x = 0 (c) C : x = y (b) C : y = 0 (d) C : y = x² (a) (b) (c) (d)

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A: Given: Suppose that Q(x, y) is a function such that 1/Q(x, y) is continuous for all (x, y). To Find:…

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A: Topic = Limits

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Q: a) estimate fx (1,0) and fy (1,0), explain b) estimate fx (0,0) and fy (0,0), explain

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A: Please find attachment for the details solution

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Q: A. Show that f(x, y) = (x-1)(y-2) (x-1)²+(y-2)² 7 (x, y) = (1,2) (x, y) = (1,2) at (1,2). 1 is…

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Q: Consider the function f(x)=1/x+4. a) As x→−∞, f(x)→ b)As x→∞, f(x)→

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Q: (@) Explain why f(z) = 5z"- 6+ Zcos z-z'e the function is entire?

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Q: x²-y² x²+y2 (x, y) = (0,0) For which value of "a" the function f (x,y) is continuous? (x, y) = (0,0)

A: Continuity.

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Q: Suppose f: X→Y, and A, B CY. Prove that (a) f-¹(AUB) = ƒ−¹(A) U ƒ−¹(B). (b) f-¹(ANB) = f¯¹(A) n…

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