.Consider the function f(7,4) = { xy x²+4y? if (x, y) # (0,0) if (x, y) = (0,0) O Is f continuous at (0,0)? Justify your answer. af ) Compute af (0,0) if they exist there. ду (0,0),

Q: Determine whether the function t(xry, 2)=x' +y-2 (where Y,/ and Ź are s tritly greater than 0) is…

A: Use Hessian matrix

Q: Choose the gradient of the function \(f\) defined by f(x y) √1 (4x 5y)². O None of the others 4x+5y…

A:

Q: Is g = {(x, y) ∈ [−5, 5] × R : x^2 + y^2 = 25} a function from [−5, 5] to R.

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Q: of of Find and for the furction f(xy,z) = x y+ y + xỉ ôx 'ay

A: For the function f( x, y, z ) = x2y + y2 + xz2 . We need to find some partial derivatives.

Q: If f(x, y) = In (2x-3y), then find of ||

A: We can solve this problem using partial derivatives.

Q: ye-(²²+y²+z²). Find all points (x, y, z) such that Vf(x, Y, z) = Question 2. Consider the function…

A:

Q: suppose that f (u, v) = ue", where u =rs and v =r + s. The composite function f(u, v) is equal to:…

A: A composite function is one which is made of other functions or in other words function values are…

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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 f be a function of two variables such that Vf(x, y) and f(2,1) 4 = af • If, in addition, x =…

A:

Q: Find the adjoint of F:C3 tends to C3 defined by F(z1, z2, z3)=(2z1+(1-i)z2 , (3+2i)z1 -4iz3 ,…

A:

Q: Suppose that y is a function of u, u is a function of x, and u = -1 when x = 2. If du/dx|x=2 = 3 and…

A: Solution

Q: Determine if f(x, y) is continuous at (0,0) where x²y² √x² + y² 0 f(x, y) =. if (x,y) = (0,0) if (x,…

A: To determine whether  is continuous at where

Q: If f (s Continuous then on -fex) True or felse?

A:

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: Let f (x, y) = Vy – 2x Evaluate f(3, 10)

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Q: Check that the equation x³ + y³ + 2³ = x + y + z implicitly defines at least one differentiable…

A:

Q: f(x) = 2/1/2 and g(x)=3x+1, find the following: b) (gof)(x) 8. Let f(x)= a) (fog)(x) c) (fof)(x) d)…

A: according to bartleby guide line we do only first part of multiple questions given  f(x)=1x2  and…

Q: for a -1 2x +5 f (x) = If fis the function defined above, then f' (-1) is A -2 B 3. E) nonexistent…

A:

Q: Let f: R2 R2 be the function given by f(x, y) = (x + y, y). Prove or →>> 8. disprove: f is…

A: Function which is one to one

Q: ) Verify the continuity of the function f(x, y) 26– 2x -- y at the point (2,-3).

A:

Q: 10. Let F(x, y, z)= y-yz+1 £z+r-z z+xy-y Find a function g such that F = √g.

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Q: O Determine if f(x, y) is continuous at (0, 0) where x² y ² f(x, y)=√x² + y² 0 if (x, y) = (0,0) if…

A:

Q: 9. Find div F if F(x, y, z) = x²yi + xyzj - x²y²k. A. 2xy + yz - 2xy² B. x² + xy C. 2xy - xz D. 2xy…

A:

Q: 5. Show that the functions x, x² interval [-1,1]. x are mutually orthogonal in the -

A:

Q: 7. F- dr from (0,0) to (3,9) along the curve y=x' if F(x, y, z) = 4 xyi + 3xy'j Evaluate

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Q: c) Which of the following functions are analytic in 121² 2 2: 42²26649 (ii) Z²-1 Z-√√Z²74

A:

Q: ) Find an analytic function f(z) = u(xr, y) + iv(r, y) with real part -. -----) u(r, y) = x? – y? +…

A:

Q: Let f(x, y) ƒ(2, 1) = = 150 - 2x² - 4y2. Evaluate f(2, 1). Give answer in exact form. 138

A: given  f(x,y)=150-2x2-4y2for  f(2,1) , put x=2  and y=1 in f(x,y)

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)…

A: