Find a potential function for F. F 8xi + y 3-4x² 2 V -j {(x,y): y > 0}

Q: f(x,y) = e (3x² + 3y2)

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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: Find the Integrating factor of: dy + y. sec5x = tan5x dx 1 (sec5x + tan5x) 5 O sec5х — tanп5x + 5 O…

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Q: 2) Differentiate and simplify: f(t) = 2et e2t+ 1

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Q: Solve ux – uy +yu = 0, where u is a function of x and y. %3D

A: Given: ux-uy+yu=0. The objective is to solve u, where u is a function of x and y.

Q: Eliminate the constant: 3x 3x y=c₁e³x. + + c₂2 ve ³x схе 3 Oy" + 6y' +9y=0 Oy"-6y'+9y=0 Oy"-4y+3y=0…

A: It is given that,y=c1e3x+c2xe3xwe need to eliminate the constants c1 and c2

Q: Graph and shade the domain of f(x, y) = vy + x² – 2.

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Q: What is the domain of h(x, y) = Vx - y?

A: Given: hx,y=x-y we know that for domain of square root function inside of root not has to be greater…

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

A: Using green's theorem.

Q: dy as a function of x. Write the function in the form y = f(u) and u= g(x). Then find y = (- 2x +8)…

A: We know that ,  if y = f ( u ) and u = g ( x )  Then  dy / dx = f ' ( u ) • g ' ( x )

Q: Find the Zero and its oodex for the function flz)=1- Ti+Z+

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Q: Q1: If w-f(z)=z'-z²+2z+2 find u and y and calculate the value of f at z-1-21. V.

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Q: Q.2 Find DivF and curlF at point (1,2) , where f(x, y) = xy² + Inxy

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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: 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: dy_ sec²y 1- 1+x² 2 when x=0 O y=

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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: |(0,3) C1:x2 + y? = 9. (-3,0) C2 (3,0) Figure 1 Based on Figure 1 and given that F = y²i + (3xy +…

A: We have to find the work done by the vector force F =y2i+(3xy+4x)j Where c is a smooth circle…

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: 2х-1 given f(x,y) = e Find y ôyôx

A: We have to find the partial derivative with respect to x and then with respect  to y of the given…

Q: y = v1 - x2 from a = 0 to r = ;

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