For which value of k is the function x+y? f(x, y) = { 2-Vx² +y² +4 , (x,y)#(0,0) k (x,y)= (0,0) continuous at every point (x,y)eR ? (a) 1 (b) -2 (c) -4 (d) 6 (e) 8

Q: 3. Find fz and fy where f(x,y) = In(x + y²).

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Q: (xy(x²-y²) Let f(x, y) =} (x²+y²) (x, y) ± (0,0)| show that fxy (0,0) + f yx(0,0) (x, y) = (0,0)

A: This question is taken from the partial derivative in which we have to prove the given statement. We…

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A: Given fx,y=lnx3y6     at (4, 3) The linear approximation in 2 variables is given by Lx, y=fa,…

Q: 9. Use the chain rule for multivariable functions to find where f(u, v) = u + v u(x, v, z) = x+y,…

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Q: du -xy du Ifu =f(x² +2yz,y² +2zx) Prove that (y- zx)-(x² - yz) -NX ду

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Q: xyz 3. If f(x, y,z)= In| +e 2 find f,, f, and f..

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Q: 23. Find the most general antiderivative of the functions: a) f(x) = 1 –- x³ + 5x5 – 3x7. 5 – 4.x3 +…

A: Given: 1.fx=1-x3+5x5-3x7 2.g(x)=5-4x3+3x6x6 we want to calculate the antiderivative is nothing but…

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Q: Find the direction at which the function f(x, y, z) = x In(e - cz) increases fastest at (-3, C O (0,…

A: To Find: The direction at which the function  fx,y,z=x ln(ey -xz) increases fastest at ( -3, 0 ,0)…

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Q: 4. a) Find an approximation for f (x, y) = at the point (1.97,1.02). V10-r-5y b) Check Euler's…

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Q: 3. Consider f : R2 → R defined by f(x,y) = y³ + 3x²y – 6x² – 6y? + 2. - (a) Determine the critical…

A: The given function is: f(x,y)=y3+3x2y-6x2-6y2+2

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Q: 2 3 tegral of the function xy d by x = 0, y = 0, z = C %3D %3D (2(5)

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Q: Find a function f (x, y, z) such that ∇f =〈z, 2y,x〉.

A: Given that, ∇f=z,2y,x We have to find a function f(x, y, z) such that ∇f=z,2y,x. Let us consider,…

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A: Consider the given information

Q: (2) Let f(x, y, z) = xy + yz + x²z². What is the maximum rate of change of f at (1,2, 3)?

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Q: (xy(x²–y²) f(x, y) = { (x²+y²) (x, y) # (0,0) (x, y) = (0,0) ) show that fxy(0,0) f yx(0,0) Let

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Q: The function f(x, y) = 1 + x² + y² at the point (0,0) is local max صواب İhi

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Q: Q2 (A) At what points f(x, y, z) in which the function f(x, y, z) = continuous? is

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Q: Find the domain of the function f(x,y)=V13032-x + y-> {(x,y) E R2 | y# x2 and ys 13032}. O {(x,y) E…

A: Given, fx, y=13032-x+1y-x2

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Q: Q4: Find f for f(x,y,z) = xcos(y + 3z) + xyz at the point ( 1,3,-1)

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Q: lim, f(x)= 0, then | f(x)dx diverges

A: Statement:  limx→∞ f(x)≠0,  then ∫1∞ f(x) dx   diverges.

Q: 1. Integrate the function f(x, y) = x – y over the triangle T with vertices (0,0), (1,0), and (1,2).

A: Given triangular region is bound by the vertices 0,0, 1,0 and 1,2. The sides of the given triangular…

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Q: Let f(x,y)=x°-4y where 0<x <1 and 0sysl. Find the minimam of value of f(x,y).

A: Answer

Q: (d) The function x²+y? Vx2+y? (x, y) # (0,0) f(x, y) (x, y) = (0,0) is continuous at (0,0).

A: Note: according to Bartleby policy we are allowed to write only one question please post remaining…

Q: (a) If F(v² – x²,v² – y², v² – z²) = 0 where v is a function of x, y,z show that 1 dv 1dv 1 dv 1 хдх…

A: Using chain rule.

Q: Show that f(z) = x³+i(1−y)³ is differentiable only at x = 0, y = 1 and f'(z) = 0.

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Q: Q1. (a) Find the points (x ,y, z) in space, where the function f(x, y,z) = /x² +y² -1 Is continuous.

A: Given :- The points x,y,z in space , where the function f x,y,z = x2 +y2 -1 is continuous.

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Q: Find the linear approximation of the function at the give f(x.y) = 3x y at (- 6,9) O A. L(x,y) = -…

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Q: e-(z-1)2-y 1 (r, y) # (1,0) If f(r, y) = (I-1)2+y (r, y) = (1,0) %3D is continuous at (1,0), what is…

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Q: xY 2. (a) Prove that the function f(x, y) is differentiable everywhere in its do- %3D x2 + y? main.

A: Solution is given below:

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A: Given function is      f(x,y,z) = ln(64-4x2-16y2-z2) We have to find the domain of this function.

Q: 1. How do you find the linearization of f(x) at x = a? Illustrate with a concrete example

A: We have to solve

Q: (d) The function x²+y? Vx²+y? (x, y) ± (0,0) f(x, y) = (x, y) = (0,0) is continuous at (0,0).

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the direction at which the function f(x, y, z) = x In(e' – xz) increases fastest at (-3,0, (0,…

A: Sorry I cannot recognize your given points. So I provide only methods of problem you can easily…