Answer the following questions given the function f below. ху if (x,y) # (0,0) f(x,y) = X +y if (x,y) = (0,0) a. Is f continuous at (0,0)? b. Is f differentiable at (0,0)? c. If possible, evaluate fy (0,0) and f, (0,0).

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A: f:ℝ2→ℝ and g: ℝ2→ℝ f is C2 Hf4,5=2-1-13 g is defined by gx,y=fx-y,yx

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A: Given that:  Tangents at point (1, 2) are:  <2, 0, 8> and <0, -1/3, 2>

Q: Given the function f(x,y)=- 4y? find each of the following. SIMPLIFY A) f.(x,y) =.

A: Note: We are allowed to answer only first three parts of the multiple questions asked. Please post…

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A:

Q: Let f (x, y) and g(x, y) be functions of two variables withthe property that ∂ f/∂x= ∂g/∂x and ∂…

A: Given: f(x, y)  and g(x, y) be functions of two variables with the property that ∂g∂x = ∂g∂x and…

Q: Let (x, y) E R × R. Consider the following functions from R? to R? a((x, y)) = (-x, y) and b((x, y))…

A: Order of the function

Q: QUESTION 6 Consider the function f(r, y, z) = 6x² + 4xy+ e4yz af Then is equal to: ду O A. 4x +…

A: we find out partial derivative with respect to y.   see 2nd step.

Q: Suppose f is a differentiable function of x and y, and g(r, s) = f(2r - s, s² - 7r). Use the table…

A: ​gr​(7,6)=−50gs​(7,6)=93​Explanation:Step 1:​Given a Table of values of f,g and fx​,fy​​​To find:…

Q: Suppose f is a differentiable function of x and y, and g(r, s) = f(2r – s, s - 3r). Use the table of…

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Q: me please: Suppose X1, X2 ∼ Unif(0, 1) and are independent. Let

A: We have given that X1, X2 ∼ Unif(0, 1)

Q: Suppose f is a differentiable function of x and y, and g(r, s) = f(4r-s, s2 - 9r). Use the table of…

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Q: 9z 21. Answer the following questions given the function f below. xy if (x.y) # (0,0) f(x,y) = x+y?…

A: As there are multiple parts of this question and you didn't mentioned which part the question's…

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A: Function which is one to one

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Q: Consider the function f(r, y) = 212 + ry – 6ry + 5x +2. (a) Show that (1,3) is a stationary point of…

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Q: 32. (Refer to the graph of f below) On which interval is f concave upward? y4 y= f(x) -2 6 x 8 -2…

A: The solution are next step

Q: Q5. Find the directional derivative of the function [f(x, y, z) = xy + y.z + z.x] at the point 1-z…

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Q: I. Determine whether or not the function x2 + 2y if (x, y) # (0,0) f(x, y) 1 er-y if (x, y) = (0,0)…

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