Consider F and C below. F(x, y, z) = yzexi + ex² + xyek, C: r(t) = (t² + 5)i + (t² − 1)j + (t² − 2t) k, Osts 2 (a) Find a function f such that F = Vf. f(x, y, z) = /F. (b) Use part (a) to evaluate F. dr along the given curve C.

Q: Find fxx (x,y), fxy(x,y), fyx (x,y), and fyy(x,y) for the function f. f(x,y) = 5x e 8xy

A: Given function is f(x, y) = 5xe8xy

Q: Find f, (x.y) and f, (x,y). Then, find f, (1,-3) and f,(-1,- 2). f(x,y) = - 5xy + 2y +6

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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: evaluate the function at the given point. f(x,y)=x2+y2, D={(x,y):0<=x<=1, 0<=y<=1}

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Q: For the function, evaluate the following. f(x, y) = 0.6x + 0.3y – 0.03xy (a) f(0, 0) (b) f(1, 0) (c)…

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Q: For the function f(x,y,z) = In (8x + 7y+ 10z), find fy, fy, and f,. fx fy =D Iz =

A: given,      fx,y,z=log8x+7y+10z

Q: 15.8 Consider the equation x³ + 3y² + 4xz² – 3z²y = 1. Does this equation define z as a function of…

A: Given:  The equation: x3 + 3y2 + 4xz2 - 3z2y = 1. To define: z in the equation as a function of x…

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

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Q: let f(x)= x2 . Find the value c in the interval (0,3) so that fave = f(c).

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Q: Find R f(x, y) dA where f(x, y) = 3x + 1 and R = [1, 2] × [−2, 4]. SSR f(x, y) dA = Submit answer…

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Q: Write the Linear Approximation to f(x, y) = x(1 + y)-¹ at (a, b) = (8, 1) in the form f(a+h,b+k)…

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Q: . Find div(F x G) = V · (F × G). F(x, y, z) = i + 9xj + 3yk G(x, y, z) = xi - yj + zk div(F x G) =

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: Find all values of x and y such that f (x, y) = 0 and fy(x, y) = 0 simultaneously. f(x, y) = x² +…

A: The given function .The aim is to find all values of  and  such that .

Q: Consider F and C below. F(x, y, z) = yzexZi + e²j + xye*²k, C: r(t) = (2 + 4)i + (t² – 1)j + (t² -…

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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: Express the given function using unit step function: 0st4 A.) f (t) = t – t u (t – 4) – 2u (t – 4)…

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Q: Find all values of x and y such that f(x, y) = 0 and f(x, y) = 0 simultaneously. f(x, y) = x² + 4xy…

A: To find all values of  such that  simutaneously.

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

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