Consider F and C below. F(x, y, z) = yzex² i + exZj + xyexz k, C: r(t) = (t² + 2)i + (t² − 2)j + (t² − 3t)k, 0≤t≤ 3 (a) Find a function f such that F = Vf. f(x, y, z) = (b) Use part (a) to evaluate J F. dr along the given curve C.

Q: Let F(u, v) be a function of two variables. Find a formula for f′(x) when             (a) f(x) =…

A: Given fx=F4x-4hence u=4x , v=4f'x=∂F∂u.∂u∂x+∂F∂v.∂v∂xBy chain rule      =∂F∂u.∂∂x4x+∂F∂u.∂∂x4…

Q: The domain of the function f (x, y) x2+5x+1 is x2 -1 A R? - { (1,y)} B R2 – { (1,y), (-1,y)} C R2 -…

A: Let f:D→E be a function then domain of f is D. Moreover, domain of f is where the function f is well…

Q: 4x + y² R² → R²: f(x, y) = 2xy +1) If there exists a function F(x, y). such that VF(x, y) = f (x,…

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Q: Determine the expression for F(x, y, z) given the function F(x, y, z) = 2x²y = xz² + 3y²z.

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Q: For the function, evaluate the following. f(x, y) = x2 – y – xy + 2 (a) f(0, 0) (b) f(1, 0) (с) f(0,…

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Q: The domain of the function f(x,y)= V1-x²-y² +In(x²+y² – 1) is empty Select one: O True O False

A: we have to find the domain for f(x)

Q: f(x+y)=f(x)+f(y)

A: First we claim then prove that claim.

Q: For the function f(x,y) = 7x² + 6y², find f(x + h,y)-f(x,y) = h f(x+h,y)-f(x,y) h

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Q: Consider f(x) = 3|x|, which is in R[-2, 2]. %3D b. Use the function F(x) to find ſ², f.

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Q: Let f(x, y) : V 125 – 3x? – 2y² - Evaluate f(1, 2)

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Q: Find f, and f, for f(x, y) = 10(9x – 8y+ 12)°. fx(Xx.y) = f,(x.y) D

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Q: Find the line integral of F along the parabola y = x² from the origin to (4, 16).

A: Using green's theorem.

Q: Find the largest domain (in R²) for the function 1+ Vr+ Vỹ x² + y² f(x, y) : =

A: Given: The function f(x, y)=1+x+yx2+y2.

Q: Given a function f(x,y,z) = 5x² In (7y + 3z). Find the domain of the function. %3D o {(xy,z) |z >…

A: Use logarithms definition to choose the correct answer.

Q: Find V x F for F(x, y, z)= - -xZ + y² i+ -yz x² + y² =j+√x² + y²k.

A:

Q: Evaluate f(х, у) ds. f(x, у) %3D у + 3 s: r(u, v) = ui + vj + 4vk, 0 sus 1, 0svs 4

A: Given: fx,y=y+3 S:ru,v=ui+vj+4vk, 0≤u≤1, 0≤v≤4 Differentiating r with respect to u, ru=1,0,0…

Q: For the function f(x,y) = In (7x+2y), find and əx dy

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Q: b. Find and sketch the domain of f(x, y, z) = Vz-x² – y²

A: (b) domain of function f(x,y,z) is set of those values of x,y,z where function f(x,y,z) is defined…

Q: Find fax, fay and fry for the function f(x, y) = (1+x+y)e¯xy Select one: a. None of these b. fxx –…

A: Consider the given function : f(x,y)=(1+x+y)e-xy

Q: b) If it is possible, find the function f(x, y) = u(x, y) + iv(x, y). where u(x, y) = x2 + 2xy- y²…

A: That's easy. Have a great day!!!

Q: he function f(x)=3x2+2x

A: Introduction: A function is bijective if it is both injective and surjective and a function f(x) is…

Q: The domain of the function f (x, y) = In(2 – /x² + y² ) is:

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Q: Find fx and fy for f(x,y) = y In (x + 8y). || fy = y x+8y

A: Step 1: Step 2: Step 3: Step 4:

Q: 2 f 2 f Consider the function f(x, t) = (x - ct)4+ (x + ct)4 where c is a constant. Calculate Əx²…

A:

Q: Given the function f(x, y) = V10 – x + y, evaluate f(2, 1) and f(-9, –3).

A: Given: fx,y=10-x+y for finding value of f2,1, we put x=2,y=1 in given expression so,…

Q: Consider the function f(x, y) = x² – 6x + y? –- 2y + 10. Sketch the domain of the function h defined…

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Q: The domain of the function f(x, y) = is {(x,y) € R? : y 2 -x} Vy+x صواب İhi

A: