Determine (x, y) and 2(x, y), where f(x, y) = X sen(xy) %3D y

Q: What is the integrating factor of y' = x - 2y? O 2x €2x Ox²

A:

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

A:

Q: The integrating factor of + 2.xy= 5x² is dx dy а. b. x2 e 2 C. 1 d. et

A:

Q: Find the antiderivative F(x) that satisfies the given condition. dF dx = 4e* + 4x²; F(0) = -5

A: Given query is to solve the differential equation.

Q: Find an antiderivative F(x) with F ′(x) = f(x) and F(0) = 0. Is there only one possible solution?.…

A: Given, F'x =fx  fx = 2+4x+5x2   We have to find Fx

Q: Evaluate 3xz dV where E = {(x, y, z) | 1 < æ < 3, x < y < 2æ, 0 < z < x + 3y}

A: ∬∫Ef(x,y,z) dV = ∫x=ex=f∫y=cy=d∫z=az=b f(x,y,z)dzdydx                                where , E…

Q: e function f(x, y) = (x – 1)² + (y – 1)² subject to the constriant

A: The given function is f(x,y)=x-12+y-12 and subjects to the constraint x2+y2=8 the formula for the…

Q: Evaluate /// (x + y – 5z) dV Where - E = {(x, y, z) | - 6 < y < 0,0 < ¤ < y,0 < z < x + y²}

A: The given integral is: I=∫∫∫E(x+y-5z) dV where E=(x,y,z) | -6≤y≤0,  0≤x≤y,  0&lt;z&lt;x+y2

Q: fm üli f (x,y,z)=x'+x*y *z ' + yz ?

A:

Q: The function f(x) = x^3 + 2xy^2 - (y^4)/x is homogeneous of what degree?

A:

Q: i $ 6x³e**+3 dx. Using integration by parts (S udv = uv – f vdu) and letting u = f(x), dv = 3g(x)dx,…

A: Using integration by parts

Q: Find fæxyzz for f(x, y, z) = z³y² ln(x). [Show your solution.] Select one: O O O x² 6z²y x² 2z³y x²…

A: See this solution in below.

Q: Verify Young's Theorem y? x2 z = In(2x + y) + +e(x+2y) y

A:

Q: d²y y = f(x) and x = e', prove that = xf'(x) +x²f"(x). %3D %3D dx2

A:

Q: Solve for the antiderivative of the function f(x) = C. *++3x + C A. ++9x+C B. 즉++9x +C D. 2x ++3x +…

A:

Q: 3xz dV where E: {(x, y, z) | 0 < r < 2, x < y < 2x, 0 < z < x + 3y} Evaluate E

A:

Q: Integrate f(x, y)

A: The region is defined as, Consider the conversion formulae from cartesian to polar coordinates,…

Q: y4) + 2y" + y = 0

A:

Q: Find fzyx. 8.8 f(x, y, z) = x*y°z® +xy³ + y°z f zyz ||

A: GIVEN: f(x, y, z) = x4 y8 z8 + xy5 + y5 z

Q: \+etari), find f.. S, and f.- xyz 3. If f(x,y,z)= hn 2

A: We have to find fx , fy , fz.

Q: sume that w = and f (x) = e . Find and dt ds II II

A:

Q: 4. 2a y' = y (y² + 3x?)

A: For the solution follow the next steps.

Q: 2. [f 5y ey dA, F- {(x, y): 0 s x s y?, 0 s ys 2} F

A:

Q: Evaluate 3xz dV where E {(x, y, z) | 2 < x < 5, x < y < 2æ, 0 < z < x + 2y}

A: Given,

Q: Find the I.F of 2y(x^2-y+x)dx+(x^2-2y)dy=0

A: Please see the answer below

Q: .Determine if F(x, y) = (2xy + y-2)i + (x² – 2xy-3)j for y > 0 is conservative.

A:

Q: Integrate f(x, y) = y(x² + y³) 3 over the domain x² + y° 0.

A: Given function is fx,y=yx2+y23 and domain is x2+y2≤4 with y≥0 We have to integrate fx,y=yx2+y23 over…

Q: Find the (absolute) maximum and minimum values of f(x, y) = sin x cos y on the square R = {(x, y)|0…

A: Given,            f(x, y)= sinxcosy                    (1) on the sqaure             R=x, y| 0≤x≤2π,…

Q: Find fr and fy- f(x, y) = 7e dt f-(x, y) = f,(x, y) =

A:

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

A:

Q: SI, (x2 + y2 + z²) dxdydz , where T: 0<x < v4 – x², 0 < y < 2, /x² + y² < z< J4 – x² – y2

A:

Q: Find f, (x,y) and fy (x.y), and explain why f(x,y) has no local extrema. f(x.y) = 8x + 3y + 4. fy…

A: It is partial derivative

Q: Let f (x, y) = r³ + y? – critical points of f . 4xy + 3x + 2y+5. Find and classify all

A:

Q: Evaluate //| (x + y – 2z) dV where E = {(x, y, z) | - 2 < y < 0,0 < x < y, 0 < z < x + y²}

A: A detailed solution is given below.

Q: Find the linear approximation to h(x) = Vx at x = 2. Use the linear approximation to approximate the…

A: Given: hx=x4 To approximate the values of 34 and 44 using linear approximation of hx. Note: the…

Q: Find fa, fy, and fz. f(x, y, z) = 5z ln(x³y³ cos(z)) fx = fy fz f₂ = =

A:

Q: Given f(x, y) = y ln(5x 6y), find f-(x, y) = fy(x, y) =

A: The function is given by fx,y = yln5x-6y To evaluate : The expression of fxx,y and fyx,y.

Q: f(x,y) = x2 + 2xy - y? is an example of homogeneous function. OTRUE O FALSE TRUE FALSE

A:

Q: [2xy + yz (i) F(x,y, z) = x2 + xz with domain R³. || xY

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

Q: ution of yl = x+xy2 W

A:

Q: dy + ydx %3D = 3x²y?dx,

A:

Q: The dimensions x and y of an object are related to its volume V by the formula V=9x2y How is dV/dt…

A:

Q: Find an antiderivative F(x) of f(x) = 5x – Va. F(æ) =|

A:

Q: Find fa, fy, and fz. f(x, y, z) = 3z ln (x³y³ cos(2z)) fx= fy= f₂ = =

A:

Q: f(x, y) = /32² + 3y fz(4, 5) = VT23 %3D

A:

Q: Find f(3,4) for f (x, y) = ln(x + Vx² + y²).

A: We have to find out the derivative

Q: – 4z) dV where E {(x, y, z) | 0 < y < 1,0 < x < y, 0 < z < x + y²} Evaluate + Y E

A: We just need to put the limits and then integrate as following

Q: Find all values of x and y such that fx = 0 and fy = 0 simultaneously. 13. f(x,y) = e*»+y?

A:

Q: 4) f(x,y) =Vx +y Ans. f.= +y Vx + y?

A: