Consider f(x, y) = 57x2 +61ry+ 7y? f-(x, y) = %3D and fy(x, y) = %3D

Q: dy x +1 xy %3D dx

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Q: Find the extrema of f(x,y) = xy + 14 subject to  x2 + y2 = 18.

A: To Determine: Find the extrema of f(x,y) = xy + 14 subject to                         x2 + y2 = 18.…

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

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Q: What is the antiderivative of f'(x) = 14x + 4 f(x) = What particular solution satisfies f( – 3) =…

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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: √²¹ fő fő¹¹ (x + y + z) dz dy dx 0

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Q: Integrate f(x, y) = 4c®* - 0.5y using h = 0.5 with y(0) = 2 from x =0 to 0.5.

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Q: Let f (x, y) = xy2 + 5. Evaluate df/dy at (x, y) = (2, -1) and interpret your result.

A: Given: f (x, y) = xy2 + 5.

Q: What is the integrating factor of 2y (y - r) dy = dr? %3D O y? 2y

A: Topic = Differential equation

Q: dy Let y = (x2 – vx)4". Find using any method. dx -

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Q: Given f(x, y) = 3æ'y- 8ry. Compute: www dy?

A: This question can be solved using the concept of partial derivatives.

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

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Q: (b) Integrate f(x, y) = 4e0.8x - 0.5y using h = 0.5 with y(0) 2 from x = 0 to 0.5.

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Q: find fy CX,Y) it (x,Y)=x2-8xy- 2y?

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Q: Find the total differential. w = (3x + 4y)/(y + 3z)

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Q: I-x² f (x, y, 2) dz dy dx 1-x² Jo

A: we have to find the region of integration

Q: The total derivative of the function ƒ(x,y) =2x²y– xy is df = (2x² – x)dx +(4xy – y)dy b. df = (4x –…

A: df  = (df(x,y)/dx)dx + (df(x,y)/dy)dy f(x,y) = 2x^2y - xy df(x,y)/dx = 4xy - y df(x,y)/dy = 2x^2 - x

Q: b) Given z = f(x -y, 2x - 2y, 3x – 3y). Show that dz dz 0. ду

A: The solution is given as

Q: find given f (x, y) = eª + 2xy² – 4y at (0, 3) af dy'

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Q: Using the linear approximation of f (x, y) near (x, y) = (1, 0) tells us that f (0.98, 0.05) is…

A: The linear approximation of a function f(x, y) at (a, b) is L(x, y) = f(a, b) + fx(a, b)(x − a) +…

Q: Q4: Given: d²y =[f(x-t)dt -show that = f (x)· dx? y %3D .2

A: Differentiation of integration

Q: b. y = cosh(arctan 3x) C. y = 4a/ cosh a d²y d. for x = 4v2t2 + a, y = a² – t² dx2 %3| -

A: Given functions are  b) y=cosh(arctan3x) c) y=4acosha d) d2ydx2 for x=42t2+a , y=a2-t2

Q: Find fr, fy and fz. f(x, y, z) = x – Vy² + z? |

A: Given f(x,y,z)=x-y2+z2. The objective is to find fx,fy and fz.

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

A: Please see the answer below

Q: Consider the finction f(x,y) = x² + xy – 5x – y+ 1. Then:

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

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Q: dy + 2xy = f(x), y(0) = 4, where xp Sx, 0sx<< 1 f(x) lo, x 2 1 0 < x< 1 y = x 2 1

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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: of find 4x + 9y of and dy For the function f(x,y) = %3D of dx ||

A: We can answer this question as below

Q: dy - f *P, = 7 dt y(0) = 4.

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Q: 2. Find the most general antiderivative of f(x) = 3+22 %3D

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Q: find given f (x, y) = e² + 2xy² – 4y at (0,3) af dy'

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Q: LLL- (x+ y+ z)dydxdz. -1 J-1 J-1 |

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Q: Find fy and fy: f(x,y) = - 3 e 4x-5y f,(x,y) = D

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Q: find for x=1 the y value for partivular solutiom, (D^2+3D-10)y=0, when x=0, y=0 and x=2, y =1

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Q: Find fr and fy- f (x, y) = | 5e dt %3| fa(x, y) = fy(x, y) =

A: We apply fundamental theorem of calculas and solve it.

Q: -2x 11/E valuate the integral 2 é V1-

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Q: Q2: Find the double integration ff (4x + 2)dydx D={(x,y):0<x<2,xẻ<y<2x}

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Q: а. max f (x, y) %3D 4x + 3ху + у S. t. х+4y— 29 3D 0 х+ 4у — 29 — 0

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Q: dy + ydx %3D = 3x²y?dx,

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Q: The antiderivative of the function f(2) +7z is

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Q: D SS f(x,y,z) dV = f(x,y,z) dx dy dz

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Q: ². I = fő fő fő (x + y + z) dx dy dz

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

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Q: Obtain the general solution using separation of variables dx = t(1 + t²)sec²x dt

A: Given: The differential equation dx=t1+t2sec2x dt . The given differential equation can be…

Q: Determine the constant of integration of f (x) = S (15z* – 3x²) dæ if ƒ (1) = 4?

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