Consider F and C below. F(x, y, z)= yzexi + exzj + xyek, C: r(t) = (²+1)i + (t² − 2)j + (t² − 3t) k, Osts3 (a) Find a function f such that F = Vf. f(x, y, z)=yez + h(z) | (b) Use part (a) to evaluate X 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 V. (F x G), if F(x, y, z) = 16xi +j+8yk and G(x, y, z) = xi + yj - zk.

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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: 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: Given: f(x, y) = arctan Find: F ƒ(x, y) dxdy x² - y² (x² + y²)² 3²-x² (x² + y²)² -y³ (y³ + xy²)² y²…

A: Given: fx, y=arctanxyTo Find: ∂2fx, y∂x∂y

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: Show that ƒ(z) = 3x² + 2x − 3y² − 1 +i (6xy + 2y) is differentiable at every point in the plan -

A: The given function is f(z)=3x2+2x-3y2-1+i(6xy+2y)...(i).

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

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Q: J 5(x) =-J5 (x) ylgn O ihi O

A: See solution below. We used properties pf bessels function.

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

A: Given function:To find Known facts:

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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Q: | Find all the poles of poles of 1 f(z) = ₂1² f(z) z3-1 and their residues.

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Q: Express the given function using unit step function: (t ,0st<4 f (t) = |2 , t2 4 A.) f (t) =t+t u (t…

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Q: C: r(t) = (t2 + 4)i + (t2 – 1)j + (t2 – 2t)k, 0sts 2 (a) Find a function f such that F = Vf. f(x, y,…

A: