Let f(x,y) = x - 2xy – y“. Compute f(3,0) and f(3, – 7).

Q: Find ôf af of and дх ду dz f(x, y, z) = 3×EYZ + 7yexz af -7 Əx af 7 ду af 3xe"y + 7yex %3D X ze

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Q: f(x.y) =e^sin(y) + In(xy) ; әз of Әхд-у

A: Given: fx,y=exsiny+lnxy To find the partial derivative of ∂3f∂x∂2y Partial differentiation: Partial…

Q: Find fæ, fy, and fz. 4,5 f(x, y, 2) = 4z In (a*y° cos(5z))

A: We can answer all the three question as below.

Q: compute ∫_∂D(x^2ydx+xy^2dy, where D is described by 0≤x≤1, 0≤y≤x

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Q: Let f(x, y) = - 4xy² – 2x² + 8y². Find and classify the critical points of f.

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Q: Let f (x, y) = 2x3 + x2y - y2. Compute d2f/dx2, d2f/dy2, and d2f/dxdy at (x, y) = (1, 2).

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Q: Sx, ifx 1 f(x) = Show that f is R- integrable.

A: R- integrable function

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: -Find the D.f ofr (x, y) = (x² – y)' at Po(3, 1) with

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Q: Let z = f(x, y) = 5x – x³ + 2xy – y². - Find and classify all the critical point(s) of this…

A: Differentiate the function fx,y=5x-x3+2xy-y2 partially with respect to x and y, to obtain fx and fy.…

Q: Let F (x) = (1 + t2)/4 dt - Then %3D F'(x) =

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Q: Let F(z, v)-v +y+3z+1-0

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Q: Verify that [(y- 2x \dx +(2xy +x*dy = [S -川- dA where C is the bounda ôy R defined by y = 0, x = 1,…

A: See the details solution in below

Q: Integrate f(æ, y) = e2=² + 2y² over the domain {(x, y) | æ² + y? < 3}

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Q: Q2: Expand f(x,y) = [sin (x y³)]² about (5, 1).

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Q: Let f(x,y)=3x2-2xy+y2-8y  Find the absolute extrema over [0,1]x[0,2]

A: Consider the given function fx,y=3x2-2xy+y2-8y First, find the partial derivatives of the function…

Q: 2. Find frxz for f(x, y,z)= z² e³xy

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Q: xy ,show that: x- y If z = = 0

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Q: Find fx , fy and fz. 1 -1 f(x, y, z) = tan %3D \xy²z4, ().

A: Here we will find Fx,Fy,Fz;

Q: Let f (x,y) =In Then f „(1, – 1) =... 3x²+ 4y3

A: This is a problem of partial.

Q: Let f(x,y)=3x2-2xy+y2-8y  Find the absolute extrema over [0,1]x[0,2].

A: We have f(x, y)=3x2-2xy+y2-8y find critical points ∂f∂x=6x-2y=0 ... (1)∂f∂y=-2x+2y-8=0  ...(2)solve…

Q: 4. Use the linearization of f(x, y) Vx + 2y to approximate f(3.01,2

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Q: of of and ду Find f(x,y) = Vx + 3y?

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

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Q: Find f, and f,. f(x, y) = 13x In xy

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Q: of For the function f(x.y) = In (x + 6y), find- of and dy

A: It is partial derivative so when we differentiate with respect to one variable consider other…

Q: If f(x) I (t° + 2t + 6) dt 0. then %3D = (x), ,f

A: The function needs to be integrated first and then to the subsequent function we will be double…

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: 7. Let f(x, y) = 10x³y* + 21xy². Find fyyy. .3,4

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Q: Let f(x, y) = ln (3x + y2). Show that fxy = fyx

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Q: If f(x,v) = ex In(5xy) find dy?

A: Given: fx,y=ex2ln5xy. To find: ∂2f∂y2 Solution: In partial derivative we differentiate with respect…

Q: of Let f(x,y) = xy° +7. Evaluate at (x,y) = (-7,1) and interpret the results. ду -

A: In this question we have find δfδy at (x, y)=(-7, 1)

Q: Let f(x, y) = 6e sin(7y) af af dy

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Q: Let f(x, y) = 7e2" sin(5y) af af dy

A: We can make it easier for you

Q: Find f, and f, for f(x,y)=y In (3x +4y). fx fy

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: Let f (x, y) = 2x³ + 4y³ + 19xy Find D = frx · fyy - fey at the point (2,2)

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Q: 2. Let F(x) = re* %3D VE dt, find F'(x). t2+sint

A: Solution is given below:

Q: If x2 + y2 = z2, find dy/dt when x = 3, y = 4, dx/dt = 2, and dz/dt = 2. (Enter your answers as a…

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Q: Find fzyz. f (x, y, z) = x°y°z° + xy° + y°z %3D 6-

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Q: Suppose that f(x, y) = e¯4z² - ly + 7z + 2y then find the discriminant of f.

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Q: Let f(x,y)=x°-4y where 0<x <1 and 0sysl. Find the minimam of value of f(x,y).

A: Answer

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: Determine the of : In (xy²) = x y dx

A: Derivative dydx of equation  lnxy2=xy

Q: Let f(x,y) = xcosy – ye*y. fry at (1,0)is equal to: -1 -5

A: fx is partial derivative with respect to x fy is partial derivative with respect to y

Q: Let L(r) be the linearization of f(x) = sin x + 1 at the point x = . Find L(π/2).

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Q: Let f(x,y) = 5x² + 6y² + 3xy – 5x – 8y + 36 What is the first coordinate of the critical point?

A: Given data:   The given expression of the function is f(x,y)=5x2+6y2+3xy-5x-8y+36.     Equate the…

Q: Find the linearization of the function f (x) = =° at z = 1. L (1) = Using this linearlization, ƒ…

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